Math in Focus

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Cumulative Review Chapters 5 and 6 to score better marks in the exam.

Math in Focus Grade 4 Cumulative Review Chapters 5 and 6 Answer Key

Concepts and Skills
Complete. Use the data in the table. (Lesson 5.1)

The ages of four cousins are shown.
8, 12, 10, 6

Question 1.
The sum of their ages is ___ years.
Answer:
Sum of their ages = 36 years.

Explanation:
The ages of four cousins are shown.
8, 12, 10, 6
Sum of their ages = 8 + 12 + 10 + 6
= 20 + 10 + 6
= 30 + 6
= 36 years.

Question 2.
The mean age of the cousins is ___ years.
Answer:
Mean age of their ages = 9 years.

Explanation:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are.
Sum of their ages = 36 years.
Number of people = 4.
Mean age of their ages = Sum of their ages ÷ Number of people
= 36 ÷ 4
= 9 years.

Answer each question. Use the data in the line plot. (Lesson 5.2)
A group of hikers made a line plot to show the number of mountains they climbed. Each ✗ represents one hiker.

Question 3.
What is the median number of mountains climbed? ____
Answer:
Median number of mountains climbed = 4.

Explanation:
Number of mountain hikers = 1 1 1 2 3 3 3 3 4 4 5 5 5 6 6 6 6 6
Median number of mountains climbed = (4 + 4) ÷ 2
= 8 ÷ 2
= 4.

Question 4.
What is the range of the set of data? ____
Answer:
The range of the set of data = 1 to 6.

Explanation:
The range of a set of data is the difference between the highest and lowest values in the set.
Number of mountain hikers = 1 1 1 2 3 3 3 3 4 4 5 5 5 6 6 6 6

Question 5.
What is the mode of the set of data? ____
Answer:
The mode of the set of data = 6.

Explanation:
The mode is the value that appears most often in a set of data values.
1 mountain climbed by 3 people.
2 mountain climbed by 1 person.
3 mountain climbed by 4 people.
4 mountain climbed by 2 people.
5 mountain climbed by 3 people.
6 mountain climbed by 5 people.

Make a stem-and-leaf plot to show the data. (Lesson 5.3)
Question 6.
A group of friends went bowling and recorded these scores.
75 73 79 84 98 64 84 67

Answer:

Explanation:
Arrange the scores given: 64 67 73 75 79 84 84 98.
To make a stem and leaf plot, each observed value must first be separated into its two parts:

Complete. Use the data in your stem-and-leaf plot.
Question 7.
____ is the mode.
Answer:
84 is the mode.

Explanation:
Scores given: 64 67 73 75 79 84 84 98.
64 – 1
67 – 1
73 – 1
75 – 1
79 – 1
84 – 2
98 – 1.

Question 8.
___ is the median.
Answer:
77 is the median.

Explanation:
Scores given: 64 67 73 75 79 84 84 98.
Median = (75 + 79) ÷ 2
= 154 ÷ 2
= 77.

Question 9.
___ is the range.
Answer:
64 to 98 is the range.

Explanation:
Scores given: 64 67 73 75 79 84 84 98.

Question 10.
___ is an outlier.
Answer:
84 to 98 is an outlier.

Explanation:
84 – 79 = 5.
73 – 67 = 6.
98 – 84 = 14.

Question 11.
How do the mode and median each change if you disregard the outlier?
Answer:
The effect of removing one outlier data point from the set. No matter what value we add to the set, the mean, median, and mode will shift by that amount but the range and the IQR will remain the same.

Explanation:
Outlier is an extreme value in a set of data which is much higher or lower than the other numbers. Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.

Write more likely, less likely, equally likely, certain, or impossible. (Lesson 5.4)
A bag has 8 blue marbles and 2 orange marbles. Describe the likelihood of each outcome.
Question 12.
An orange marble is chosen. _____
Answer:
Probability of orange marbles is chosen = 1 ÷ 5 or \(\frac{1}{5}\) .

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Total marbles in bag = 8 + 2 = 10.
Probability of orange marbles is chosen = Number of orange marbles ÷ Total marbles in bag
= 2 ÷ 10
= 1 ÷ 5 or \(\frac{1}{5}\) .

Question 13.
A blue marble is chosen. ____
Answer:
Probability of blue marbles is chosen = 4 ÷ 5 or \(\frac{4}{5}\) .

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Total marbles in bag = 8 + 2 = 10.
Probability of blue marbles is chosen = Number of blue marbles ÷ Total marbles in bag
= 8 ÷ 10
= 4 ÷ 5 or \(\frac{4}{5}\) .

Question 14.
A red marble is chosen. ____
Answer:
Probability of red marbles is chosen = 0.

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Number of red marbles = 0.
Total marbles in bag = 8 + 2 = 10.
Probability of red marbles is chosen = Number of red marbles ÷ Total marbles in bag
= 0 ÷ 10
= 0.

Question 15.
A blue or an orange marble is chosen. ____
Answer:
Probability of orange or blue marbles is chosen = 1.

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Total marbles in bag = 8 + 2 = 10.
Probability of blue marbles is chosen = Number of blue marbles ÷ Total marbles in bag
= 8 ÷ 10
= 4 ÷ 5 or \(\frac{4}{5}\) .
Probability of orange marbles is chosen = Number of orange marbles ÷ Total marbles in bag
= 2 ÷ 10
= 1 ÷ 5 or \(\frac{1}{5}\) .
Probability of orange or blue marbles is chosen = (Number of orange marbles + Number of blue marbles) ÷ Total marbles in bag)
= (8 + 2) ÷ 10
= 10÷ 10
= 1.

Solve. Use the scenario above. (Lesson 5.4)
Question 16.
How would you change the number of each colored marble in the bag so that it is more likely that an orange marble is chosen?
Answer:

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Total marbles in bag = 8 + 2 = 10.

Look at the spinner. Write the probability of each outcome as a fraction. (Lesson 5.5)

Question 17.
Probability of landing on 2 = ____
Answer:
Probability of landing on 2 = 2 ÷ 3 or \(\frac{2}{3}\)

Explanation:
Number of 2 on spinner = 4.
Total numbers on spinner = 6.
Probability of landing on 2 = Number of 2 on spinner ÷ Total numbers on spinner
= 4 ÷ 6
= 2 ÷ 3 or \(\frac{2}{3}\)

Question 18.
Probability of landing on 6 = ____
Answer:
Probability of landing on 6 = 0.

Explanation:
Number of 6 on spinner = 0.
Total numbers on spinner = 6.
Probability of landing on 6 = Number of 6 on spinner ÷ Total numbers on spinner
= 0 ÷ 6
= 0.

Add or subtract. Write each answer in simplest form. (Lessons 6.1 and 6.2)
Question 19.
\(\frac{3}{4}\) + \(\frac{1}{12}\) + \(\frac{1}{6}\) =
Answer:
\(\frac{3}{4}\) + \(\frac{1}{12}\) + \(\frac{1}{6}\) = \(\frac{11}{12}\)

Explanation:
\(\frac{3}{4}\) + \(\frac{1}{12}\) + \(\frac{1}{6}\) =
= [(9 + 1) ÷ 12] + \(\frac{1}{12}\)
= \(\frac{10}{12}\) + \(\frac{1}{12}\)
= (10 + 1) ÷ 12
= \(\frac{11}{12}\)

Question 20.
\(\frac{9}{10}\) – \(\frac{1}{5}\) – \(\frac{1}{2}\) =
Answer:
\(\frac{9}{10}\) – \(\frac{1}{5}\) – \(\frac{1}{2}\) = \(\frac{1}{5}\)

Explanation:
\(\frac{9}{10}\) – \(\frac{1}{5}\) – \(\frac{1}{2}\) =
= [(9 – 2) ÷ 10] – \(\frac{1}{2}\)
= \(\frac{7}{10}\) – \(\frac{1}{2}\)
= (7 – 5) ÷ 10
= 2 ÷ 10
= \(\frac{1}{5}\)

Write the amount of water in each set of 1-liter containers as a mixed number. (Lesson 6.3)
Question 21.

Answer:
Amount of 2 jars = 1 \(\frac{1}{5}\)L.

Explanation:
Amount of water in first jar = 1L.
Amount of water in second jar = \(\frac{1}{5}\)L.
Amount of 2 jars = Amount of water in first jar + Amount of water in second jar
= 1 + \(\frac{1}{5}\)
= (5 + 1) ÷ 5
= \(\frac{6}{5}\)
= 1 \(\frac{1}{5}\)L.

Question 22.

Answer:
Amount of three jars = 2\(\frac{1}{2}\)L.

Explanation:
Amount of water in first jar = 1L.
Amount of water in second jar = 1L.
Amount of water in third jar = \(\frac{1}{2}\)L.
Amount of three jars = Amount of water in first jar + Amount of water in second jar + Amount of water in third jar
= 1 + 1 + \(\frac{1}{2}\)
= 2 + \(\frac{1}{2}\)
= (4 + 1) ÷ 2
= \(\frac{5}{2}\)
= 2\(\frac{1}{2}\)L.

Express the shaded part of each figure as a mixed number or an improper fraction. (Lessons 6.4 and 6.5)
Question 23.

Answer:

Explanation:
Mixed number of the shaded figure = 2\(\frac{3{4}\)
Improper fraction of the shaded figure = (8 + 3) ÷ 4
= 11 ÷ 4 or \(\frac{11}{4}\)

Question 24.

Answer:

Explanation:
Improper fraction of the shaded figure = \(\frac{12}{8}\)
Mixed number of the shaded figure = \(\frac{12}{8}\)
= 1\(\frac{4}{8}\)

Express each improper fraction as a mixed number. (Lesson 6.5)
Question 25.
\(\frac{9}{7}\) = ____
Answer:
\(\frac{9}{7}\) = 1\(\frac{2}{7}\)

Explanation:
\(\frac{9}{7}\) = 1\(\frac{2}{7}\)

Question 26.
\(\frac{20}{9}\) = ____
Answer:
\(\frac{20}{9}\) = 2\(\frac{2}{9}\)

Explanation:
\(\frac{20}{9}\) = 2\(\frac{2}{9}\)

Express each mixed number as an improper fraction. (Lesson 6.5)
Question 27.
3\(\frac{2}{5}\) = ____
Answer:
3\(\frac{2}{5}\) = \(\frac{17}{5}\)

Explanation:
3\(\frac{2}{5}\) = (15 + 2 ) ÷ 5 = \(\frac{17}{5}\)

Question 28.
2\(\frac{8}{9}\) = ____
Answer:
2\(\frac{8}{9}\) = \(\frac{26}{9}\)

Explanation:
2\(\frac{8}{9}\) = (18 + 8) ÷ 9 = \(\frac{26}{9}\)

Add or subtract. (Lesson 6.6)
Question 29.
2 + \(\frac{2}{5}\) + \(\frac{1}{10}\) = ____
Answer:
2 + \(\frac{2}{5}\) + \(\frac{1}{10}\) = \(\frac{25}{10}\)

Explanation:
2 + \(\frac{2}{5}\) + \(\frac{1}{10}\) = ](10 + 2) 5] + \(\frac{1}{10}\)
= \(\frac{12}{5}\) + \(\frac{1}{10}\)
= (24 + 1) ÷ 10
= \(\frac{25}{10}\)

Question 30.
3 – \(\frac{3}{4}\) – \(\frac{5}{8}\) = ___
Answer:
3 – \(\frac{3}{4}\) – \(\frac{5}{8}\) = \(\frac{23}{8}\)

Explanation:
3 – \(\frac{3}{4}\) – \(\frac{5}{8}\) = 3 – [(6 – 5)÷ 8]
= 3 – \(\frac{1}{8}\)
= (24 – 1) ÷ 8
= \(\frac{23}{8}\)

check (✓) each set in which \(\frac{2}{5}\) of the figures are shaded. (Lesson 6.7)
Question 31

Answer:

Explanation:
(✓) each set in which \(\frac{2}{5}\) of the figures are shaded.
Fraction of square figure = Number of shaded squares ÷ Total number of squares
= 8 ÷ 16
= 1 ÷ 2 or \(\frac{1}{2}\)
Fraction of circle figure = Number of shaded circles ÷ Total number of circles
= 6 ÷ 15
= 2 ÷ 5 or \(\frac{2}{5}\)
Fraction of triangle figure = Number of shaded triangles ÷ Total number of triangles
= 4 ÷ 20
= 1 ÷ 5 or \(\frac{1}{5}\)

Solve. (Lesson 6.7)
Question 32.
\(\frac{2}{3}\) of 15 = ___
Answer:
\(\frac{2}{3}\) of 15 = 10.

Explanation:
\(\frac{2}{3}\) of 15 = 2 ×5 = 10.

Question 33.
\(\frac{3}{5}\) of 40 = ___
Answer:
\(\frac{3}{5}\) of 40 = 24.

Explanation:
\(\frac{3}{5}\) of 40 = 3 × 8 = 24.

Problem Solving
Solve. Show your work.
Question 34.
Teams A, B, C, and D were in a tournament. The average score of the 4 teams was 92. Team A scored 78 points,
Team B scored 95 points, and Team C scored 88 points.

a. How many points did Team D score?
Answer:
Points Team D scored = 107.

Explanation:
Points Team A scored = 78.
Points Team B scored = 95.
Points Team C scored = 88.
Points Team D  scored = ??.
The average score of the 4 teams was 92.
=> (Points Team A scored + Points Team B scored + Points Team C scored  + Points Team D scored) ÷ 4 = 92.
=> (78 + 95 + 88 + ??) ÷ 4 = 92.
=> (173 + 88 + ??) ÷ 4 = 92.
=> (261 + ??) ÷ 4 = 92 × 4
=> 261 + ?? = 92 × 4
=> 261 + ?? = 368.
=> ?? = 368 – 261
=> ?? = 107.
Points Team D scored = 107.

b. Find the range of the scores. Hence, state the difference in score between the winning team and the losing team.
Answer:
Range of the scores = 78 to 107.
29 is the difference in score between the winning team and the losing team.

Explanation:
Scores scored by teams = 78 88 95 107.
Points Team A scored = 78.
Points Team B scored = 95.
Points Team C scored = 88.
Points Team D  scored = 107.
Difference:
Highest score scored – Least score scored
= 107 – 78
= 29.
Losing team are Team A,B,C. Winning team is A.

Question 35.
Michael scored 15, 21, and 24 in the first three basketball games of the season.
a. What is his mean score?
Answer:
His mean score = 20.

Explanation:
Score scored by Michael in the first three basketball games of the season = 15, 21, 24.
The mean is the arithmetic average of a set of given numbers. The median is the middle score in a set of given numbers. The mode is the most frequently occurring score in a set of given numbers.
His mean score = score scored ÷ Number of games
= (15 + 21 + 24) ÷ 3
= (36 + 24) ÷ 3
= 60 ÷ 3
= 20.

b. What is the range of his scores?
Answer:
Range of his scores = 15 to 24.

Explanation:
Score scored by Michael in the first three basketball games of the season = 15, 21, 24.
Range of his scores = 15 to 24.

c. How many points must he score in the next game to achieve a mean score of 27?
Answer:
48 more points must he score in the next game to achieve a mean score of 27.

Explanation:
His mean score = score scored ÷ Number of games
=> 27 = (15 + 21 + 24 + ?? ) ÷ 4
=> 27 = (36 + 24 + ?? ) ÷ 4
=> 27 = (60 + ?? ) ÷ 4
=> 27 × 4 = 60 + ??
=> 108 – 60 = ??
=> 48 = ??.

Question 36.
Samuel and Kenneth collect sports cards. The average number of cards they have is 248. Samuel has 3 times as many cards as Kenneth. How many cards does each boy have?
Answer:
Number of sports cards Kenneth collected = 124.
Number of sports cards Samuel collected = 372.

Explanation:
Samuel has 3 times as many cards as Kenneth.
Let Number of sports cards Kenneth collected be X.
=> Number of sports cards Samuel collected = 3 × Number of sports cards Kenneth collected
= 3  × X = 3X.
The average number of cards they have is 248.
=> (Number of sports cards Samuel collected + Number of sports cards Kenneth collected) ÷ 2 = 248.
=> (3X + X) ÷ 2 = 248
=> 4X ÷ 2 = 248.
=> 4X = 248 × 2
=> 4X = 496.
=> X = 496 ÷ 4
=> X = 124.
Number of sports cards Samuel collected = 3X = 3 × 124 = 372.

Question 37.
A group of students made a list of the states where they were born. The line plot shows the number of times the letter A’ appears in the name of each state. Each ✗ represents one state.

Complete. Use the data in the line plot.
a. What is the mode of the set of data? ____
Answer:
Mode of the set of data = 1.

Explanation:
Number of times A appears in states = 0 1 1 1 2 2 3 4 4
The mode is the most frequently occurring score in a set of given numbers.
Mode of the set of data = 1.

b. What is the mean number of times the letter A’ appears? ___
Answer:
Mean number of times the letter A’ appears = 2.

Explanation:
The mean is the arithmetic average of a set of given numbers.
Number of times A appears in states = 0 1 1 1 2 2 3 4 4
mean number of times the letter A’ appears = (0 + 1 + 1 + 1 + 2 + 2 + 3 + 4 + 4) ÷ 9
= 18 ÷ 9
= 2.

c. Is the name of a state more likely to have 1 or 2 As? Explain your answer.
Answer:
Yes, the state going to have more likely 2As because mean number of times the letter A’ appears = 2.

Explanation:
Yes state is going to have 2 As because average letters in the states name going to be 2 that menas in their names 2As are likely to be.

d. According to the data, what is less likely to happen? Explain your answer.
Answer:
According to the data, its less likely to happen that minimum As likely to be 1 and maximum 2 As in every name of state not more.

Explanation:
Well, its less likely to happen that minimum As likely to be 1 and maximum 2 As in every name of state not more.

Question 38.
The stem-and-leaf plot shows the number of pages in 8 books.

a. Which stem has only odd numbers for its leaves?
Answer:
Stem 3 is having only odd numbers for its leaves.

Explanation:
All the numbers ending with 1,3,5,7 and 9 are odd numbers. For example, numbers such as 11, 23, 35, 47 etc.
Stem 2 – 1 5
Stem 3 – 0 5 5 7.
Stem 4 – 3 6.

b. Find the median of the set of data.
Answer:
Median of set = 35.

Explanation:

Number of pages = 21, 25, 30, 35, 35, 37, 43, 46.
Median of set = (35 + 35) ÷ 2
= 70 ÷ 2
= 35.

c. Find the mode of the set of data. ___
Answer:
Mode of the set of data = 35.

Explanation:
The mode is the value that appears most often in a set of data values.
Number of pages = 21, 25, 30, 35, 35, 37, 43, 46.

21 – 1 time.
25 – 1 time.
30 – 1 time.
35 – 2 time.
37 – 1 time.
43 – 1 time.
46 – 1 time.

d. Find the range of the set of data. ____
Answer:
Range of the set of data – 21 to 46.

Explanation:
Number of pages = 21, 25, 30, 35, 35, 37, 43, 46.

e. Which of the above measures tells you the difference in the number of pages between the thickest and the thinnest books? ___
Answer:
Range of the set of data above measures tells you the difference in the number of pages between the thickest and the thinnest books.

Explanation:
Range of the set of data above measures tells you the difference in the number of pages between the thickest and the thinnest books.

f. Is there an outlier in the set of data? Explain your answer. ___
Answer:
No, there is no outlier in the set of data because there is no much difference in the data measurements.

Explanation:
There is no outlier in the set of data because there is no much difference in the data measurements.

Question 39.
A cube is numbered from 1 to 6 and tossed once. What is the probability of tossing
a. a 5 or a 6? ___
Answer:
Probability of tossing 5 = 1 ÷ 6 or \(\frac{1}{6}\)
Probability of tossing 6 = 1 ÷ 6 or \(\frac{1}{6}\)

Explanation:
A cube is numbered from 1 to 6 and tossed once.
Total numbers on cube = 6.
Probability of tossing 5 = Number of 5 side ÷ Total numbers on cube
= 1 ÷ 6 or \(\frac{1}{6}\)
Probability of tossing 6 = Number of 6 side ÷ Total numbers on cube
= 1 ÷ 6 or \(\frac{1}{6}\)

b. an odd number? ___
Answer:
Probability of odd number = 1 ÷ 2 or \(\frac{1}{2}\)

Explanation:
odd number on cube = 1, 3 , 5.
Total numbers on cube = 6.
Probability of odd number = odd number on cube ÷ Total numbers on cube
= 3 ÷ 6
= 1 ÷ 2 or \(\frac{1}{2}\)

Question 40.
Sasha has 40 stamps in her collection. 12 of them are from foreign countries.

a. What fraction of the stamps are foreign stamps?
Answer:
Fraction of the stamps are foreign stamps = 3 ÷ 10 or  \(\frac{3}{10}\)

Explanation:
Number of stamps in her collection Sasha has = 40.
Number of stamps of them are from foreign countries = 12.
Fraction of the stamps are foreign stamps = Number of stamps of them are from foreign countries ÷ Number of stamps in her collection Sasha has
= 12 ÷ 40
= 3 ÷ 10 or  \(\frac{3}{10}\)

b. What fraction of the stamps are U.S. stamps?
Answer:
3 ÷ 10 or  \(\frac{3}{10}\)  are fraction of the stamps are U.S. stamps.

Explanation:
Fraction of the stamps are U.S. stamps = Number of stamps of them are from U.S.  countries ÷ Number of stamps in her collection Sasha has
= 12 ÷ 40
= 3 ÷ 10 or  \(\frac{3}{10}\)

Question 41.
A string is 1 foot long. Blake cuts What fraction of the string is left?
Answer:

Explanation:
Length of the string = 1 foot.

Question 42.
Pedro scored \(\frac{1}{4}\) of all the goals scored during a soccer game. He scored 2 goals. How many goals were not scored by Pedro?
Answer:
Number of goals were not scored by Pedro = 6.

Explanation:
Points scored by Pedro \(\frac{1}{4}\) of all the goals scored during a soccer game.
Let all goals be X.
Points soccer game scored = X × \(\frac{1}{4}\) = 2.
=> X = 2 × 4
=> X = 8.
Points Pedro scored = 2.
Number of goals were not scored by Pedro = Points soccer game scored – Points Pedro scored
= 8 – 2
= 6.

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This handy Math in Focus Grade 3 Workbook Answer Key Chapter 15 Practice 1 Measuring Length provides detailed solutions for the textbook questions.

Math in Focus Grade 3 Chapter 15 Practice 1 Answer Key Measuring Length

Measure each to the nearest inch.

Example

Question 1.

Answer:

Explanation:
In the above image we can observe Ruler and Rope B. The length of the Rope B is calculated by using Ruler.
The length of rope B is more than 4 inches but less than 5 inches long. It is nearer to 4 inches than to 5 inches. So, the length of Rope B is about 4 inches.

Question 2.

Rope C is about ___________ inches.
Answer:

Explanation:
In the above image we can observe Ruler and Rope C. The length of the Rope C is calculated by using Ruler.
The length of rope C is more than 1 inch long. It is nearer to 2 inches than 1 inch. So, the length of Rope C is about 2 inches.

Question 3.

Rope D is about ___________ inches.
Answer:

Explanation:
In the above image we can observe Ruler and Rope D. The length of the Rope D is calculated by using Ruler.
The length of rope D is in between 2 and 3 inches. So, the length of Rope D is about 2.5 inches.

Measure each ribbon to the nearest half-inch.

Example

Question 4.

Ribbon B is about __________ inches long.
Answer:

Explanation:
In the above image we can observe Ruler and Ribbon B. The length of the Ribbon B is calculated by using Ruler.
The length of ribbon B is more than 3 1/2 inches. It is nearer to 4 inches than 3 inches. So, the length of Ribbon B is about 4 inches long.

Question 5.

Ribbon C is about __________ inches long.
Answer:

Explanation:
In the above image we can observe Ruler and Ribbon C. The length of the Ribbon C is calculated by using Ruler.
The length of Ribbon C is more than 2 inches but less than 2 1/2 inches. It is nearer to 2 1/2 inches than 2 inches. So, the length of Ribbon C is about 2 1/2 inches long.

Question 6.

Ribbon D is about __________ inches long.
Answer:

Explanation:
In the above image we can observe Ruler and Ribbon D. The length of the Ribbon D is calculated by using Ruler.
The length of Ribbon D is more than 5 1/2 inches but less than 6 inches. It is nearer to 6 inches than 5 1/2 inches. So, the length of Ribbon D is about 6 inches long.

Question 7.

Ribbon E is about __________ inches long.
Answer:

Explanation:
In the above image we can observe Ruler and Ribbon E. The length of the Ribbon E is calculated by using Ruler.
The length of Ribbon E is more than 4 1/2 inches but less than 5 inches. It is nearer to 5 inches than 4 1/2 inches. So, the length of Ribbon E is about 5 inches long.

Question 8.

Ribbon F is about __________ inches long.
Answer:

Explanation:
In the above image we can observe Ruler and Ribbon F. The length of the Ribbon F is calculated by using Ruler
The length of Ribbon F is more than 4 inches but less than 5 inches. It is at 4 1/2 inches. So, the length of Ribbon F is about 4.5 inches long.

Estimate the length of each object to the nearest half-inch.

Question 9.
Bracelet A is about _________ quarters long.
Answer:
Bracelet A is about 3 quarters long.

Question 10.
It is about ___________ inches long.
Answer:
It is about 3 inches long.
Explanation:
In the above image we can observe one quarter is 1 inch wide. There are 3 quarters. It is about 3 inches long.

Question 11.
Bracelet B is about ___________ quarters long.
Answer:
Bracelet B is about 5 quarters long.

Question 12.
It is about __________ inches long.
Answer:
It is about 5 inches long.
Explanation:
In the above image we can observe one quarter is 1 inch wide. There are 5 quarters. It is about 5 inches long.

Estimate the length of each object to the nearest half-inch.

Question 13.
Craft stick C is about ___________ buttons long.
Answer:
Craft stick C is about 3 buttons long.

Question 14.
It is about ___________ inches long.
Answer:
It is about 1 1/2 inches long.
Explanation:
In the above image we can observe one button is 1/2 inch wide. There are 3 buttons. It is about 1 1/2 inches long.

Estimate the length of each object to the nearest half-inch.

Question 15.
Craft stick D is about ___________ buttons long.
Answer:
Craft stick D is about 4 buttons long.

Question 16.
It is about ___________ inches long.
Answer:
It is about 2 inches long.
Explanation:
In the above image we can observe one button is 1/2 inch wide. There are 4 buttons. It is about 2 inches long.

Fill in the blanks. These are 12-inch rulers.

Question 17.
1 ft = ____________ in.
Answer:
1 feet = 12 inch

Question 18.
1 yd = ___________ ft = ___________ in.
Answer:
1 yard = 3 feet = 36 inches
Explanation:
In the above image we can observe 1 feet is equal to 12 inches. We know that 1 yard is equal to 3 feet.
3 x 12 = 36 inches
3 feet is equal to 36 inches.

Name 3 objects that are 1 foot long each.

Question 19.
The 3 items are ___________, ___________, and ___________.
Answer:

Name 3 objects that are longer than 1 foot but shorter than 3 feet.

Question 20.
___________, ___________, and ___________ are longer than 1 foot but shorter than 3 feet.
Answer:

Sarah is going on a treasure hunt. She is looking for objects that are about 3 feet long. 3 feet is equal to 1 yard.
Answer:

Look at the objects she has found. Then sort them in the table.

Question 21.

Answer:

Complete. Use the map to help you.

Question 22.
The distance between Camp Evergreen and Camp Birch is __________ mile.
Answer:
The distance between Camp Evergreen and Camp Birch is 1 mile.
Explanation:
In the above image we can observe the distance between Camp Evergreen and Camp Birch is 1,760 yard. We know that 1 mile is equal to 1,760 yard.

Question 23.
The distance between Camp Birch and the Bay Station is about __________ mile.
Answer:
The distance between Camp Birch and the Bay Station is about 1 mile.
Explanation:
The distance between camp Birch to camp plane is 5,170 feet.
The distance between camp plane to bay station is 107 feet.
5,170 feet + 107 feet = 5,277 feet
1 mile = 5,280 feet

Question 24.
The distance between Camp Birch and Camp Maple is __________ yards.
Answer:
The distance between Camp Birch and Camp Maple is 3 yards.
Explanation:
The distance from camp Birch to camp Maple is 9 feet.
1 yard = 3 feet
2 yards = 6 feet
3 yards = 9 feet

Question 25.
Camp __________ is nearer to the Bay Station than Camp Gum.
Answer:
Camp Plane is nearer to the Bay Station than Camp Gum.

Question 26.
The distance between Camp Plane and Camp Birch is slightly less than 1,760 ___________.
Answer:

Choose the unit that you would use to measure each. Write inch, foot, yard, or mile.

Question 27.
The length of a hiking trail ___________
Answer:
The length of a hiking trail in mile.

Question 28.
The length of an airplane ___________
Answer:
The length of an airplane in foot.

Question 29.
The height of a teacher ___________
Answer:
The height of a teacher in inch.

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Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 2 Practice 1 Using a Calculator to finish your assignments.

Math in Focus Grade 5 Chapter 2 Practice 1 Answer Key Using a Calculator

Add.

Question 1.
215 + 9,843 = ________
Answer: 10050
The addition is taking two or more numbers and adding them together, that is, it is the total sum of 2 or more numbers.
An addition sentence is a mathematical expression that shows two or more values added together and their sum.
215

The numbers that are added are called addends and the answer to addition is called the sum. In an addition sentence, the addends are added to get the sum. The numbers with more than 2 digits can also be added vertically. We always start adding from the ones digit and move towards the digits at the highest place.

Question 2.
6,789 + 18 = ____
Answer: 6807
Step 1: Write the numbers one below the other as per the places of the digits.
Step 2: Start adding from the ones digit. Write the sum under the ones digit. If the sum of the one’s digit is greater than 9, write the one’s digit of the sum under the ones and carry forward its tens digit to the tens column.
Step 3: Add the tens digits. (If there was a carry forward digit, add it along)

The numbers that are added are called addends and the answer to the addition is called the sum. In an addition sentence, the addends are added to get the sum. The numbers with more than 2 digits can also be added vertically. We always start adding from the ones digit and move towards the digits at the highest place.
6789 and 18 are the addends and the 6807 is a sum.

Question 3.
97 + 8,154 = ________
Answer: 8,251
Step 1: Write the numbers one below the other as per the places of the digits.
Step 2: Start adding from the ones digit. Write the sum under the ones digit. If the sum of the one’s digit is greater than 9, write the one’s digit of the sum under the ones and carry forward its tens digit to the tens column.
Step 3: Add the tens digits. (If there was a carry forward digit, add it along)

The numbers that are added are called addends and the answer to the addition is called the sum. In an addition sentence, the addends are added to get the sum. The numbers with more than 2 digits can also be added vertically. We always start adding from the ones digit and move towards the digits at the highest place.
8154 and 97 are the addends and the 8251 is a sum.

Question 4.
1,693 + 8,157 = ____
Answer: 9850
Step 1: Write the numbers one below the other as per the places of the digits.
Step 2: Start adding from the ones digit. Write the sum under the ones digit. If the sum of the one’s digit is greater than 9, write the one’s digit of the sum under the ones and carry forward its tens digit to the tens column.
Step 3: Add the tens digits. (If there was a carry forward digit, add it along)

The numbers that are added are called addends and the answer to the addition is called the sum. In an addition sentence, the addends are added to get the sum. The numbers with more than 2 digits can also be added vertically. We always start adding from the ones digit and move towards the digits at the highest place.
1693 and 8157 are the addends and 9850 is a sum.

Subtract.

Question 5.
8,215 – 79 = ___
Answer: 8,136
Subtraction means reducing a value from another value to get the required value.
The number 8,125 is called minuend.
The number 79 is called subtrahend.
The number 8,136 is called the difference.
8,125-79=8,136
The number you take away from is called the minuend. It is the biggest number in the equation.

Question 6.
6,286 – 129 = ____
Answer: 6157
Subtraction means reducing a value from another value to get the required value.
The number 6,286 is called minuend.
The number 129 is called subtrahend.
The number 6,157 is called the difference.
6286-129=6157
The number you take away from is called the minuend. It is the biggest number in the equation.

we need to borrow 1 to group 6 as 16 and then subtract 9 from it. Then we get 7.

Question 7.
2,159 – 1,998 = ____
Answer: 161
Subtraction means reducing a value from another value to get the required value.
The number 2,159 is called minuend.
The number 1,998 is called subtrahend.
The number 161 is called the difference.
2159-1998=161
The number you take away from is called the minuend. It is the biggest number in the equation.

We need to borrow 1 to group 1 as 11 and 5 as 15 and then subtract from it.

Question 8.
26,145 – 9,354 = ____
Answer: 16791
Subtraction means reducing a value from another value to get the required value.
The number 26,145 is called minuend.
The number 9354 is called subtrahend.
The number 16,791 is called the difference.
26,145-9,354=16,791
The number you take away from is called the minuend. It is the biggest number in the equation.

We need to borrow 1 to group 4 as 14, 1 as 11, 6 as 16 and then subtract from it.

Multiply.

Question 9.
359 × 12 = ___
Answer: 4308
In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life. The major application we can see in multiplication tables.
The multiplication of numbers say, ‘a’ and ‘b’, is stated as ‘a’ multiplied by ‘b’.
Multiplication symbol: The symbol of multiplication is denoted by a cross sign (×) and also sometimes by a dot (.).
Multiplication formula:
The multiplication formula is given by:
Multiplier × Multiplicand = Product
1. The multiplicand is the total number of objects in each group
2. The multiplier is the number of equal groups
3. Product is the result of multiplication of multiplier and multiplicand.
Rules of multiplication (how to multiply):
There are various rules to multiply numbers. They are:
1. Multiplication of two integers is an integer.
2. Any number multiplied by 0 is 0.
3. Any number multiplied by 1 is equal to the original number.
4. If an integer is multiplied by multiples of 10, then the same number of 0s are added at the end of the original number. Example: 4 × 1000 = 4000.
5. The order of the numbers, does not matter, when multiplied together. Example: 2 × 3 × 4 × 5 = 5 × 4 × 3 × 2 = 3 × 2 × 4 × 5 = 120.
Now by applying all the rules we need to calculate 359×12:

Now I multiplied 2 with 9 then I get 18 I cancelled 8 and wrote in the problem and the remaining 1 will be added to the next means I multiplied 2 with 5 then I get 10. To this 10 I added the remaining 1 to the 10 then it becomes 11 again I cancelled 1 and wrote in the problem and so on…

Question 10.
217 × 58 = ___
Answer:12,586.
Multiplication symbol: The symbol of multiplication is denoted by a cross sign (×) and also sometimes by a dot (.).
Multiplication formula:
The multiplication formula is given by:
Multiplier × Multiplicand = Product
1. The multiplicand is the total number of objects in each group
2. The multiplier is the number of equal groups
3. Product is the result of multiplication of multiplier and multiplicand.

Therefore, the answer is 12,586.

Question 11.
1,975 × 5 = ___
Answer: 9875
Multiplication symbol: The symbol of multiplication is denoted by a cross sign (×) and also sometimes by a dot (.).
Multiplication formula:
The multiplication formula is given by:
Multiplier × Multiplicand = Product
1. The multiplicand is the total number of objects in each group
2. The multiplier is the number of equal groups
3. Product is the result of multiplication of multiplier and multiplicand.

We need to add the remaining numbers to the next multiple products.

Question 12.
7,050 × 8 = ___
Answer: 56400
Multiplication symbol: The symbol of multiplication is denoted by a cross sign (×) and also sometimes by a dot (.).
Multiplication formula:
The multiplication formula is given by:
Multiplier × Multiplicand = Product
1. The multiplicand is the total number of objects in each group
2. The multiplier is the number of equal groups
3. Product is the result of multiplication of multiplier and multiplicand.

Multiplying with something with 0 will get 0. And I multiplied 8 by 5 I get 40. In 40 I cancelled 0 and the remaining 4 will be added to the next multiple products and so on… the process continues until the calculation completes.

Divide

Question 13.
504 ÷ 9 = ____
Answer: 56
Division: The meaning of divide is to separate into two or more equal parts, areas, classes, categories, groups or divisions. In simple words, the meaning of divide is to distribute the whole thing to a group in equal parts or make equal parts. Suppose, a diagonal of a square divides it into two triangles of equal area. The result of a division operation may or may not be an integer. Sometimes, the result will be in the form of decimal numbers.
Divide symbol: The symbol used to represent divide or division is ÷, slash (/) or a horizontal line ( _ ). These symbols are used as per convenience while dealing with various types of problems and calculations. Also, x/y or can be read as “x by y” or “x over y”.
Division Math Formula: The four important terms used in the division operation are dividend, divisor, quotient and remainder. The formula to calculate the division of two numbers is:
Dividend ÷ Divisor = Quotient + Remainder.
Here,
1. The dividend is the number, which is being divided
2. The divisor is the number, which divides the number (dividend) into equal parts
3. The quotient is the result of the division operation
4. The remainder is the leftover number in the division operation.
Points to Remember:
– If a number is divided by 1, the answer should be the same as the dividend. For example, 56/1 is 56.
– If the dividend and divisor are the same, then the quotient is 1. For example, 10/10 is 1.
– If a dividend is divided by 0, then the answer is undefined. For example, 15/0 is undefined.
Now by remembering all the points we calculate the division problem:

Question 14.
4,104 ÷ 6 = ___
Answer: 684
Division Math Formula: The four important terms used in the division operation are dividend, divisor, quotient and remainder. The formula to calculate the division of two numbers is:
Dividend ÷ Divisor = Quotient + Remainder.

We need to divide 4104 with 6 then we get the quotient 684 and the remainder is 0.

Question 15.
8,160 ÷ 85 = ____
Answer: 96
Division Math Formula: The four important terms used in the division operation are dividend, divisor, quotient and remainder. The formula to calculate the division of two numbers is:
Dividend ÷ Divisor = Quotient + Remainder.

96 is the quotient and 0 is the remainder.
Multiply 85 by 9 then we get 765. from 816 subtract 765 then we get 51 and in the dividend, we have 0. That 0 will get down. Then it will become 510. Again multiply 85 by 6. Then we get 510. Subtract 510 from the 510. Then it becomes 0 which is the remainder.

Question 16.
17,604 ÷ 18 = ____
Answer: 978
Division Math Formula: The four important terms used in the division operation are dividend, divisor, quotient and remainder. The formula to calculate the division of two numbers is:
Dividend ÷ Divisor = Quotient + Remainder.

In this problem also we have to multiply 18 by 9 then we get 162 and then subtract then we get 14. Now the tens place will get down then 14 becomes 140 and again multiply 18 by 7 then we get 126 again subtract 126 from 140 then we get 14 and again get down ones place 4, then 14 becomes 144. Subtract both we get 0 which is the remainder.

Only one path after each problem has the correct answer.
Trace Flavio’s path by choosing the paths with the correct answers.

Question 17.

The prize at the end of Flavio’s path is:
Answer: Football.
Flavio’s path is represented in the below diagram with the colouring:

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Math in Focus Grade 5 Chapter 2 Answer Key Whole Number and Multiplication and Division

Math Journal

Question 1.
Kelly has a 370-page sketch book. She wants to allocate an equal number of pages for making sketches to each month of the year. She uses division to find the number of pages she can possibly allocate to each month, and the number of pages she will have left over.
She works out the division like this:

Which part of the answer tells the number of pages that Kelly can possibly allocate to each month?
Which part tells the number of pages left over?
Answer:
Quotient
Remainder
Explanation:
Quotient part of the answer tells the number of pages that Kelly can possibly allocate to each month
Remainder part tells the number of pages left over

Question 2.
Mark was asked to simplify the numeric expression 6 + 4 × 2. He worked out the steps like this:
6 + 4 × 2 = 10 × 2
= 20
Is he correct? Explain why.
Answer:
No, he is not correct
Explanation:
the answer will be 8 · 6+2=8 · Order or operations. You must multiply or divide before adding or subtracting

Question 3.
Look at the following problem and the solution given by a student: Abel, Belle, and Cindy have $408 altogether. Belle has $7 more than Cindy and $5 more than Abel. How much does Abel have?

What was the mistake made? What should the correct answer be?
Answer:

Abel has 135
Explanation:
Abel has 135
408 – 9 = 399
399 divided by 3 = 133
133 + 2 = 135

Put On Your Thinking Cap!

Challenging Practice

Solve. Use any strategy.

Question 1.
A sticker costs 15¢, and a packet of 8 similar stickers costs $1. Clement buys 37 stickers. What is the least amount of money that Clement spends on the stickers?
Answer: $4 and  75¢
Explanation:
if buy Individual sticker:
37 x 15 = 555 =  $5 and 5¢
if buy packet of sticker:
37 ÷ 8 = 4 and remainder is 5
so, Clement needs to buy 4 packets and 5 stickers.
4 packets  cost is 4 x 1 = $4 and 5 stickers cost is 5 x 15 = 75
So total cost is = $4 75¢
least amount of money that Clement spends on the stickers is $4 and 75¢

Question 2.
40 members of a parents’ organization are making candles to raise money. 1 member drops out and the rest have to make 3 more candles each to make up. Each member makes the same number of candles. How many candles do they make altogether?
Answer: 4680
Explanation:
When possible, assign a variable to the value the problem wants you to find.  Here,

Solve. Use any Strategy.

Question 3.
Mr. Thomas puts up fence posts from one end of a field to the other, equal distances apart. There are 27 posts. The width of each post is 10 centimeters. The distance between two posts is 30 meters. Find the length of the fence.
Answer: 782 meters and 70 centimeters
Explanation:
There are 27 posts and puts up fence posts from one end of a field to the other, equal distances apart So total distances are 27 -1 = 26
The distance between two posts is 30 meters then total distance between posts is 26 x 30 = 780 meters
The width of each post is 10 centimeters and then total posts width is 27 x 10 =270 centimeters = 2 meters and 70 centimeters

Question 4.
Kirsten has 64 coins in her piggy bank. She has $9.25 in dimes and quarters. How many dimes and how many quarters does she have?
Answer: 45 dimes and 19 quarters
Explanation:
Let there be x dimes and 64-x quarters.
0.1x+0.25(64-x) = 9.25
0.1x+16-0.25x=9.25
-0.15x=-6.75
x= 45
64-x=64-45=19
so 45 dimes and 19 quarters

Put On Your Thinking

Problem Solving

Solve. Use any strategy.

Question 1.
Darcy, Jason, and Maria share $268. Jason has $20 more than Darcy and Maria has twice as much money as Jason. How much money do Darcy and Jason have altogether?
Answer: Darcy and Jason have altogether=$124
Explanation:
Let Darcy has money=x
Jason has $20 more than Darcy
Jason =20+x
Maria has twice as much money as Jason
Maria = 2(20+x)=40+2x
Darcy,Jason and Maria share $268
x+20+x+40+2x=268
4x+60=268
4x=208
x=52
So Darcy has money=$52
Jason has money=20+x=20+52=$72
Darcy and Jason have altogether=$(52+72)=$124

Question 2.
Juan and Rachel have the same number of marbles. Rachel gives away 10 marbles and Juan gives away 22 marbles. Rachel then has 3 times as many marbles as Juan. How many marbles did each of them have at first?
Answer: 28
Explanation:
Let X = the number of marbles that Juan or Rachel started with.
Rachel gives away 10 marbles–> X – 10 and Juan gives away 22–> X – 22
Than Rachel has 3 times as many marbles as Juan–> X-10 = 3(X-22)
X – 10 = 3X – 66
-56 =- 2X
X = 28

Solve. Use any strategy.

Question 3.
Gerry had a total of 30 pens and pencils. He decided to trade with his friends all his pens for pencils. If he traded every pen for 2 pencils, he would have 48 pencils in all. How many pens and how many pencils did he have before the trade?
Answer: 12 Pencils
Explanation:
Let p = pens
Pencils = 30-p
Total pencils after the exchange will be: 48 = 30-p + 2p
48 = 30 + p
18 = p (pens)
30-18 = 12 pencils
To check: 18×2 + 12 = 36+12 = 48

Math Journal

Multiply. Explain how you can check if your answer is reasonable.

184 × 97
Answer: 17848
200 × 100 = 20000 So 17848 is nearest number. It is reasonable.
Explanation:
184 × 97  = 17848

Math Journal

Jodi estimated these products.
a. 2,892 × 21 rounds to 3,000 × 20 = 60,000
b. 2,743 × 18 rounds to 3,000 × 20 = 60,000
She then worked out the actual answers. Even though the estimated answers were the same, Jodi found that the actual answers were very different from each other.
Answer:
2,892 × 21 =60732
2,743 × 18  =  49374

Question 1.
In which case is the estimate closer to the actual answer? Explain why.
Answer:
In case A
2,892 × 21 =60732
The Estimation is closer

Question 2.
If an estimate does not make your answer seem reasonable, what can you do to make sure you have done your work correctly?
Answer:
2,743 × 18  =  49374
We have to find the actual product
We have to round to Hundreds

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Go through the Math in Focus Grade 4 Workbook Answer Key Chapter 2 Practice 1 Estimation to finish your assignments.

Math in Focus Grade 4 Chapter 2 Practice 1 Answer Key Estimation

Find each sum or difference. Then use rounding to check that your answers are reasonable. Round each number to the nearest hundred.

Example
534 + 287
534 + 207 = 021

Add: 500 + 300 = 800
821 is close to 800.
So, the answer is reasonable.

Question 1.
515 + 342
Answer:
515 + 342=857

Now we added the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The first number is 515:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘1’.
– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 500
The second number is 342:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘4’.
– 4 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 300.

Now add both the numbers:
500+300=800
Therefore, the answer is not reasonable.
For the number 857, the round figure is 900 because in the tens place number ‘5’ is there. According to rule 2, +1 should be added to the hundreds place and the remaining places will become zero. Then it becomes 900. But here we got the estimated value of 800. That’s why it is not reasonable.

Question 2.
681 – 519
Answer:
681 – 519=162

Explanation:
Now we subtracted the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The first number is 681:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘8’.
– 8> 5,  +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.
– The rounding off number is 700.
The second number 519:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘1’.
– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 500
Now subtract both the numbers:

700-500=200
Therefore, the answer is reasonable.
168 is nearer to 200 according to rule 2.

Question 3.
170 + 725 + 333
Answer:
170 + 725 + 333=1228

Explanation:
Now we added the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The first number is 170:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘7’.
– 7 > 5,  +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.
– The rounding off number is 200.
The second number is 725:
We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘2’.
– 2 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 700
The third number is 333:
We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘3’.
– 3 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 300.

Now add all the three estimated numbers:
200+700+300=1200
Therefore, the answer is reasonable.

Question 4.
2,979 – 814
Answer:
2,979 – 814=2165
Explanation:
Now we subtracted the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The first number is 2,979:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘7’.
– 7 > 5,  +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.
– The rounding off number is 3000.
The second number is 814:
We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘1’.
– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 800
Now subtract both the numbers:

3000-800=2200
the answer is reasonable.
2,165 is nearer to 2,200.

Find each sum or difference. Then use front-end estimation to check that your answers are reasonable.

Example

Question 5.
7,930 + 2,517
Answer:
7,930 + 2,517=10,447
The answer is 10,447
Explanation:
Now we added the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The first number is 7,930:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘3’.
– 3< 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 7900.
The second number is 2,517:
We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘1’.
– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 2500
Now add the estimated values:

7900+2500=10400
10,447 is close to 10,400
So, the answer is reasonable.

Question 6.
3,166 – 1,625
Answer:
3,166 – 1,625=1541
the answer is 1,541.
Explanation:
Now we subtract the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The first number is 3,166:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘6’.
– 6> 5, +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.
– The rounding off number is 3200.
The second number is 1,625:
We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘2’.
– 2 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 1600
Now subtract the estimated values:

3,200-1,600=1,600
1541 is close to 1500, not 1600
So, the answer is not reasonable.

Question 7.
36,053 + 11,832
Answer:
36,053 + 11,832=47,885
The answer is 47,885
Explanation:
Now we add the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The first number is 36,053:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘5’.
– 5 = 5, +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.
– The rounding off number is 36,100.
The second number is 11,832:
We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘3’.
– 3 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 11,800
Now add the estimated values:

36,100+11,800=47,900
47,885 is close to 47,900
So, the answer is reasonable.

Question 8.
9,705 – 8,250
Answer:
9,705 – 8,250=1455
The answer is 1,455.
Explanation:
Now we subtract the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The first number is 9,705:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘0’.
– 0 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 9,700.
The second number is 8,250:
We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘5’.
– 5 <= 5, +1 is added to the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 8,300
Now subtract the estimated values:

9,700-8,300=1,400
1,455 is close to 1,500, not 1,400
So the answer is not reasonable.

Find each product. Then use rounding to check that your answers are reasonable. Round the 3-digit number to the nearest hundred.

Example

Question 9.
233 × 4
Answer:
233 × 4=932
The answer is 932
Explanation:
Now we multiply the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The number is 233:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘3’.
– 3 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 200.
Now multiply the estimated value by 4.
200 × 4 = 800
932 is not close to 800.
932 is close to 900
So, the answer is not reasonable.

Question 10.
485 × 2
Answer:
485 × 2 = 970
The answer is 970
Explanation:
Now we multiply the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The number is 485:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘8’.
– 8 > 5, +1 is added to the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 500.
Now multiply the estimated value by 2.
500 × 2 = 1000
970 is close to 1000.
So, the answer is reasonable.

Question 11.
117 × 5
Answer:
117 × 5 = 585
The answer is 585.
Explanation:
Now we multiply the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The number is 117:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘1’.
– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 100.
Now multiply the estimated value by 5.
100 × 5 = 500
585 is not close to 500
585 is close to 600
So, the answer is not reasonable.

Question 12.
276 × 3
Answer:
276 × 3 = 828
the answer is 828
Explanation:
Now we multiply the above-given numbers.
We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.
In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.
RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.
RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.
The number is 276:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘7’.
– 7 > 5, +1 is added to the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 300.
Now multiply the estimated value by 3.
300 × 3 = 900
828 is not close to 900
828 is close to 800
So, the answer is not reasonable.

Find each product. Then use front-end estimation to check that your answers are reasonable.

Example

Question 13.
108 × 3
Answer:
108 × 3 = 324
The answer is 324
Explanation:
Front end rounding is taking the number farther to the left and rounding it. So with our number, 108, we will be rounding to the hundreds since the farthest number to the left is a 1 and it’s in the hundredth place. The front end means the front or first digit in the number.
secondly, how do you round a number? Here’s the general rule for rounding:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
The number 108:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘0’.
– 0 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 100.
Now multiply the estimated value by 3.
100 × 3 = 300
324 is close to 300
So, the answer is reasonable.

Question 14.
121 × 5
Answer:
121 × 5 = 605
the answer is 605
Explanation:
Front end rounding is taking the number farther to the left and rounding it. So with our number, 121, we will be rounding to the hundreds since the farthest number to the left is a 1 and it’s in the hundredth place. The front end means the front or first digit in the number.
secondly, how do you round a number? Here’s the general rule for rounding:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
The number 121:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘0’.
– 2 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 100.
Now multiply the estimated value by 5.
100 × 5 = 500
605 is close to 600, not 500
So, the answer is not reasonable.

Question 15.
439 × 2
Answer:
439 × 2 = 878
the answer is 878
Explanation:
Front end rounding is taking the number farther to the left and rounding it. So with our number, 439, we will be rounding to the hundreds since the farthest number to the left is a 4 and it’s in the hundredth place. The front end means the front or first digit in the number.
secondly, how do you round a number? Here’s the general rule for rounding:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
The number 439:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘0’.
– 3 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 400.
Now multiply the estimated value by 2.
400 × 2 = 800
878 is close to 800
So, the answer is reasonable.

Question 16.
227 × 4
Answer:
227 × 4 = 908
the answer is 908.
Explanation:
Front end rounding is taking the number farther to the left and rounding it. So with our number, 439, we will be rounding to the hundreds since the farthest number to the left is a 4 and it’s in the hundredth place. The front end means the front or first digit in the number.
secondly, how do you round a number? Here’s the general rule for rounding:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
The number 227:
– We need to round off nearest to hundred so check the tens place.
– The tens place is having the digit ‘2’.
– 2 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.
– The rounding off number is 200.
Now multiply the estimated value by 4.
200 × 4 = 800
908 is not close to 800
So, the answer is not reasonable.

Find each quotient. Then use related multiplication facts to check that your answers are reasonable.

Example
85 ÷ 5
85 ÷ 5 = 17
The answer is 17.

since division is the opposite of multiplication, find a multiple of 5 that is close to 8.

5 × 10 = 50
5 × 20 = 100
85 is closer to 100 than to 50.
So, 85 ÷ 5 rounds to 100 ÷ 5.
100 ÷ 5 = 20
85 ÷ 5 is about 20.
17 is close to 20.
Answer 17 is reasonable.

Question 17.
78 ÷ 2
Answer:
78 ÷ 2 = 39
The answer is 39
since division is the opposite of multiplication, find a multiple of 2 that is close to 78.
2 × 20 = 40
2 ×30 = 60
2 × 40 = 80
78 is closer to 80
so, 78 ÷ 2 rounds to 80 ÷ 2
80 ÷ 2 = 40
78 ÷ 2 is about to 40.
39 is close to 40
Answer 39 is reasonable.

Question 18.
68 ÷ 4
Answer:

Solve. Decide whether to find an estimate or an exact answer.

Example

Danny and his 3 friends buy baseball tickets for $26 each. About how much money do they need altogether?

Because the question asks ‘about how much money they need, you can estimate.

4 × $30 = $120
They need about $120.

Question 21.
Jonathan, Shia, and Casey bought 35 toy figures. Each of the boys decides to make a team of 11 figures. Do they have enough toy figures?
Answer: yes
Explanation:
The number of toys figures they bought=35
The number of figures they want to decide to make a team=11
Now the above-given question was asked do they have enough toy figures=?
If we go for the estimation process:
35 is close to 40
11 is close to 10
If we divide both the numbers then we get the estimated answer which is close to the original answer.
The original answer:
35/11=3.18
Now do the estimation process:
40/10=4
3.18 is close to the 4.
So, the answer is reasonable.

Question 22.
A turtle hatchery collected 457 turtle eggs in a week. The next week, it collected 656 eggs. About how many eggs did the hatchery collect in the two weeks?
Answer:
The number of turtle eggs a title hatchery collected in a week=457
The number of turtles eggs a title hatchery collected in a next week=656
The number of turtle eggs he collected in two weeks=X
X=457+656
X=1113
Therefore, he collected 1113 eggs in two weeks.

Question 23.
The table shows the number of beads in Stella’s collection.

Stella needs 400 yellow beads, and 700 green beads to make a necklace. Does she have enough beads for the necklace?
Answer: yes, she could have enough beads.
The number of yellow beads Stella needs=400
The number of green beads Stella needs=700
In the above-given figure, the number of colours of beads is given.
But in the question, green beads are more than yellow beads. Moreover, the question asked was yellow and green beads are given. So according to that, we calculate the beads.
In the above-given figure:
Yellow beads=417
Green beads=609
The total number of beads=1026
In the question given:
Yellow beads=400
Green beads=700
The total number of beads=1100
So, definitely she can make necklace with the given number of beads.

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Practice the problems of Math in Focus Grade 2 Workbook Answer Key Cumulative Review Chapters 7 to 9 to score better marks in the exam.

Math in Focus Grade 2 Cumulative Review Chapters 7 to 9 Answer Key

Concepts and Skills

Fill in the blank.

Question 1.
Which is longer, 3 meters or 5 meters? ___ m
Measure the pencils.
Then fill in the blanks.

Answer: 5 meters is long.
A meter is a SI unit scientifically accepted as the base unit of distance and length. Along with other units like a kilometre or an inch, a meter is one of the fundamental units in SI. One meter equals the length of the path that a light travels in a vacuum for the time of 1/299,792,458 seconds. SI symbol for meter is m, and one meter is 100 centimetres or 1/1000^th (10^-3) of a kilometre.
5>3 so 5 metres is long.

Question 2.
Pencil A is ___ centimetres.
Answer: 300 centimetres.
Definition: Centimeter is considered a common unit of length used in SI. It is equivalent to 10 millimetres or 1/100^th (10^-2) of a meter. Years ago it was a basic unit in formerly used CGS (centimetre-gram-second) unit system, but in modern times the role of the basic unit of length is played by a meter. The symbol of centimetre is cm.
This is very easy to use a metre to centimetre converter. First of all, just type the meter (m) value in the text field of the conversion form to start converting m to cm, then select the decimals value and finally hit the convert button if auto calculation didn’t work. Centimetre value will be converted automatically as you type. The decimals value is the number of digits to be calculated or rounded of the result of meter to centimetre convert.
1 metre=100 centimetres.
Use the formula below to convert any value from meters to cm:
Centimetres=metres×100
To from meters to centimetres, you just need to multiply the value in meters by 100. (It is called the conversion factor)
Therefore, centimetres=3×100=300.

Question 3.
Pencil B is ___ centimetres.
Answer: 500 centimetres.
Explanation:
1 metre=100 centimetres.
Use the formula below to convert any value from meters to cm:
Centimetres=metres×100
To from meters to centimetres, you just need to multiply the value in meters by 100. (It is called the conversion factor)
Therefore, centimetres=5×100=500.

Question 4.
Which pencil is shorter? Pencil ______
Answer: Pencil A is shorter.

Because it is 300 cms which is lesser than pencil B.

Question 5.
How much shorter is it? ___ cm
Answer: 300 cms.
Pencil A is 300 cm shorter.

Draw. Then label.

Question 6.
Draw a line 7 centimetres long. Label it Line X.
__________
Answer:
– Construct a line L on a paper and mark A on it.
– Now place the metal point of the compass at the zero mark of the ruler.
– Make adjustments in the compass such that the pencil point is at the 7 cm mark on the ruler.
– Take compass on L such that its metal point is on A.
– Now mark a small mark as B on L which is corresponding to the pencil point of the compass.
– Here, AB is the required line segment of length 7 cm.
– The line is marked with X.

Question 7.
Draw a line 4- centimetres longer than Line X. Label it Line Y.
______________
Answer: 11 cm.
– Construct a line L on a paper and mark X on it.
– Now place the metal point of the compass at the zero mark of the ruler.
– Make adjustments in the compass such that the pencil point is at the 7 cm mark on the ruler and then mark 4 cms.
– Take compass on L such that its metal point is on X.
– Now mark a small mark as Y on L which is corresponding to the pencil point of the compass.
– Here, XY is the required line segment of length 11 cm.
– The line is marked with X and Y. And the total is 7+4=11 cm.

Fill in the blanks.

Question 8.

The books have a mass of ____ kilograms.
Answer: 3 kilograms.
Definition: kilogram (kg), the basic unit of mass in the metric system. A kilogram is very nearly equal (it was originally intended to be exactly equal) to the mass of 1,000 cubic cm of water. The pound is defined as equal to 0.45359237 kg, exactly. It is defined as being equal to the mass of the international prototype of the kilogram.
Explanation:
– It is showing the hand on 3.
– So it is 3 kgs.

Question 9.

The toy aeroplane has a mass of ___ grams.
Answer: 17 grams.
Explanation:
The weights are 10, 2, 5.
Add all the grams to get total mass. 10+2+5=17 grams.
Therefore, the toy aeroplane has a mass of 17 grams.

Fill in the blanks.

Question 10.
The chicken has a mass of ___ grams.
Answer: 550 grams.

– The gram is a unit of mass.
– One gram is one-thousandth the mass of one kilogram. The previous definition of the gram was the absolute weight of a 1-centimetre cube of pure water at 4 °C.
– The symbol for the gram is g.
– The gram is a small unit of mass. It is approximately the mass of one small paper clip.
Explanation:
– The hand is showing on after 500. And the small measurements can be written as 10,20, 20, 40, 50, 60, 70, 80, 90, and 100.
– The hand is showing on 50. So it is 550 grams.(500+50=550).

Question 11.
The duck has a mass of ____ grams.
Answer: 710 grams.
– The gram is a unit of mass.
– One gram is one-thousandth the mass of one kilogram. The previous definition of the gram was the absolute weight of a 1-centimetre cube of pure water at 4 °C.
– The symbol for the gram is g.
– The gram is a small unit of mass. It is approximately the mass of one small paper clip.
Explanation:

– The hand is showing on after 700. And the small measurements can be written as 10,20, 20, 40, 50, 60, 70, 80, 90, and 100.
– The hand is showing on 10. So it is 710 grams. (700+10=710).

Question 12.
Which is lighter? ____
Answer: Chicken.
Explanation:
The mass of chicken is 550 grams and the mass of duck is 710 grams. By comparing both grams chicken is lighter than duck because the weight of duck is more than chicken.
550<710.

Question 13.
How much lighter is it? ___ g
Answer:160 grams lighter.
Explanation:
By comparing both duck is having higher mass and the chicken is 550 gms.
To know how much lighter the chicken we need to subtract duck mass and chicken mass. Assume it as X.
X= 710-550
X=160 grams.

Fill in the blank.

Question 14.

What is the mass of the bag of rice? __ kg
Answer:7 kgs.
Definition: kilogram (kg), the basic unit of mass in the metric system. A kilogram is very nearly equal (it was originally intended to be exactly equal) to the mass of 1,000 cubic cm of water. The pound is defined as equal to 0.45359237 kg, exactly. It is defined as being equal to the mass of the international prototype of the kilogram.
Explanation:
How do I choose the bag of rice that is 7 kgs? I will explain below:

– Observe the 2nd picture, In that the total weight of potatoes are given.
– The weight of potatoes are 3kg+5kg=8kg.
– In the first picture, two different masses are there. Those are rice and potatoes.
– We already know the potatoes weight that is 8 kgs and the remaining 7 kgs are rice.

Look at the pictures. Then fill in the blank.

Question 15.

Containers A and B are the same size. Which container has a greater volume of water? Container ____
Answer: container B

Observe the pictures carefully. Containers are equal but the water in them is different volumes. Container B is having more water than Container A. So I circles Container B.

Fill in the blanks.

Containers A, B, C, and D are the same size.

Question 16.
Which container has the most water? Container ____
Answer: Container B.
Definition of volume:
– Volume is the number of shares of security traded during a given period of time.
– Generally, securities with more daily volume are more liquid than those without, since they are more “active”.
– Volume is an important indicator in technical analysis because it is used to measure the relative significance of a market move.
– The higher the volume during a price move, the more significant the move and the lower the volume during a price move, the less significant the move.
– Formula: Volume of cylinder=π · r² · h

Observe the pictures carefully. Containers are equal but the water in them is different volumes. Container B is having more water than Container A, c, and D. So I circled the B container.
Question 17.
Container ___ contains the same amount as Container ____
Answer: C and D.
Container C and Container D have the same amount of water.
– If the water is in a cylindrical container, then the volume of that water is calculated using the formula to calculate the volume of the cylinder.
– If the water is only halfway high in the container, then you’ll need to use half the height of the cylinder in the formula.
Formula: Volume=π · r² · h

Find the volume of water in each container.

Example

Question 18.

Volume of water = ___ or ____
Answer: 70 litres.
The volume of water is 70 litres or 70l.
Explanation:
– The volume of water is as good as the shape of the reservoir (container) it’s in. Often, the containers have a circular, rectangular or square cross-section.
– For a rectangular based container, we use the formula to calculate the volume of a rectangular prism also known as a cuboid.
– Formula: volume=l × b × h

– The volume of water is 70 l and each litre difference in between them is 10.

Question 19.

Volume of water = ___ or ____
Answer: 40 l
Explanation:
– The volume of water is as good as the shape of the reservoir (container) it’s in. Often, the containers have a circular, rectangular or square cross-section.
– For a rectangular based container, we use the formula to calculate the volume of a rectangular prism also known as a cuboid.
– Formula: volume=l × b × h

The volume of water is 40 litres or 40 l.

Question 20.

Volume of water = ___ or ____
Answer: 2 litres.
– If the water is in a cylindrical container, then the volume of that water is calculated using the formula to calculate the volume of the cylinder.
– If the water is only halfway high in the container, then you’ll need to use half the height of the cylinder in the formula.
Formula: Volume=π · r² · h

From the given question, the volume of water is 2 litres.

Fill in the blanks.
Use your answers for Exercises 18 to 20.

Question 21.
Which container has the greatest volume of water?
Container ____
Answer: Container B.
Explanation:

– For a rectangular based container, we use the formula to calculate the volume of a rectangular prism also known as a cuboid.
– Formula: volume=l × b × h
By comparing containers B, C, and D. Container D have the highest volume of water and is a cuboid in shape.
The volume of water is 70 litres.

Question 22.
Which container has the least volume of water?
Container ____
Answer: Container D.
– If the water is in a cylindrical container, then the volume of that water is calculated using the formula to calculate the volume of the cylinder.
– If the water is only halfway high in the container, then you’ll need to use half the height of the cylinder in the formula.
Formula: Volume=π · r² · h

It has 2 litres of water which is least to compare all the containers.

Look at the pictures.
The containers are filled with water.
Which containers contain less than 1 liter of water each? Circle each answer.

Question 23.

Answer:

Explanation:
In the above picture, the last 3 cups will have less volume because 1 litre is divided into 3 parts. So the volume is less in those 3 cups.

Problem Solving

Solve.

Draw bar models to help you.

Question 24.
Mrs. Kim’s empty suitcase has a mass of 5 kilograms. After she packs some books into the suitcase, her suitcase has a mass of 21 kilograms. What is the mass of the books?
The mass of the books is ___ kilograms.
Answer: 16 kilograms.

The mass of empty suitcase=5 kgs
The mass of filled suitcase after packing books=21 kgs.
The mass of books=X
X=21-5
X=16 kgs.

Question 25.
Seth has a ball of string. He uses 35 centimetres of string to decorate his scrapbook. He uses another 78 centimetres of string to decorate a gift.
a. How much string does he use in all?

b. If he had 200 centimetres of string at first how much string does he have now?

a. He uses ___ centimetres of string in all.

b. He has ___ centimetres of string now.
Answer:
a. He uses 113 centimetres of string in all.
Explanation:

The number of cms he used string to decorate book=35
The number of cms he used string to decorate gift=78
The total string he used for decorating book and gift=X
Add both the cms to get the total cms of string.
X=35+78
X=113 cms.
b. He has 87 centimetres of string now.
Explanation:
The total string =113 cms
If he had 200 cms at first, now the string cms are how much?. Assume it as X.
Subtract supposed cms-actual cms. Then we get the answer.
X=200-113
X=87 cms.

Question 26.
Tania’s hand puppet has a mass of 440 grams. It is 120 grams heavier than Hector’s hand puppet. What is the total mass of the two hand puppets?
The total mass of the two hand puppets is ___ grams.
Answer: 1000 grams.
Explanation:

The mass of Hector’s hand puppet=440
The mass of Tania’s hand puppet which is 120 grams more than Hector’s hand puppet=440+120=560
The total mass of two hand puppets is 560+440=1000 grams.

Question 27.
A tank contains 65 litres of oil Another 15 litres of oil are added. Later, 40 litres are poured out. What is the volume of oil in the tank in the end?
The volume of oil in the tank, in the end, is ___ litres.
Answer: 40 litres.
Explanation:

The number of litres of oil tank have=65
The number of litres added extra into the tank=15
The total number of litres of oil tank have after adding extra 15 litres=65+15=80
The number of litres poured out=40
The volume of the tank after pouring the 40 litres of oil=X
X=80-40
X=40 litres.

Question 28.
Sarah sells 27 liters of milk in the morning. She sells another 8 liters of milk in the afternoon. Ray sells 4-8 liters of milk.
a. Who sells more milk?

b. How much more?

a. ______ sells more milk.

b. sells ______ more litres of milk.
Explanation:
a. Sarah sells more milk.

The number of litres she sells in the morning=27
The number of litres she sells in the afternoon=8
The total number of litres Sarah sells=27+8=35.
The number of litres Ray sells=4-8
By comparing both of them Sarah is selling 35 litres of milk which is more than Ray.
b. sells 27 more litres of milk.
Explanation:
The total number of litres Sarah sells=35
The maximum number of litres Ray sells is totally=8.
We need to calculate the number of more litres more Sarah is selling than Ray.
Subtract the total number of litres sold by Sarah – sold by Rey
=35-8
=27.
therefore, Sarah sells 27 litres more than Rey.

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This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Properties of Triangles and Four-sided Figures provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 13 Answer Key Properties of Triangles and Four-sided Figures

Put On Your Thinking Cap!

Challenging Practice

This figure is a rhombus and ∠ADO = ∠CDO. Find the measure of ∠DOC.

Answer:
∠DOC = 90°
Explanation:
The diagonals of a rhombus bisect each other at right angles (90°)
∠DOC = 90°

Put on Your Thinking cap!

Problem Solving

Question 1.
ABCD is a trapezoid in which \(\overline{A D}\) || \(\overline{B C}\). Find the measure of ∠CED.

Answer:

Explanation:
With the help of protractor we find the Measure of ∠CED.
∠CED. = 70°

Question 2.
ABCD is a parallelogram and CDEF is a rhombus. Find the measure of ∠ADE.

Answer:

Explanation:
By using the protractor we can find the Angle of ADE
∠ADE. = 137°

Math Journal

Question 1.
A teacher asked her students to sketch and label the angles of a triangle. These are the angle measures that three students chose to draw.
Wayne: 120°, 80°, 10° Ashley: 70°, 28°, 72° Frank: 51 °, 37°, 92°
Will each student be able to draw his or her triangle? Explain your answer.
Wayne: _______
Ashley: ________
Frank: ______
Answer:
Wayne: 120°, 80°, 10° = 210°
Ashley: 70°, 28°, 72° = 170°
Frank: 51 °, 37°, 92° =  180°
Explanation:
The sum of all the angles of an triangle is equal to 180 degrees
Only Frank can draw the triangle.

Question 2.
What are two ways to identify an isosceles triangle?
Answer:
Isosceles. An isosceles triangle can be drawn in many different ways. It can be drawn to have two equal sides and two equal angles or with two acute angles and one obtuse angle.

Question 3.
Jordan is measuring the angles of a triangle. He finds out that m∠A = m∠B = 60°. Without measuring ∠C, he says that triangle ABC is an equilateral triangle. Is he correct? Explain why.

Explanation:
Yes.
The sum of all the angles of an equilateral triangle is equal to 180 degrees. As all the angles are equal to 60 degrees, the sum is equal to 60°+ 60°+ 60° =180 degrees
m∠C = 60°