Math in Focus

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 4 Practice 2 Real-World Problems: Multiplying with Proper Fractions to finish your assignments.

Math in Focus Grade 5 Chapter 4 Practice 2 Answer Key Real-World Problems: Multiplying with Proper Fractions

Solve. Draw models to help you.

Question 1.
Lena has some eggs in the refrigerator. She takes out \(\frac{3}{5}\) of the eggs to make waffles and scrambled eggs. She uses \(\frac{2}{3}\) of the eggs she took out to make waffles. What fraction of the total number of eggs does Lena use to make waffles?
Answer:
\(\frac{2}{5}\)
Explanation:
Lena has some eggs in the refrigerator.
She takes out \(\frac{3}{5}\) of the eggs to make waffles and scrambled eggs.
She uses \(\frac{2}{3}\) of the eggs she took out to make waffles.
\(\frac{3}{5}\) x \(\frac{2}{3}\)

\(\frac{2}{5}\) of the total number of eggs that Lena use to make waffles

Question 2.
Dawn has \(\frac{5}{6}\) yard of lace. She uses \(\frac{4}{5}\) of it for a dress and the rest for a jewel box. How much lace does she use for the jewel box?
Answer:
\(\frac{1}{6}\) Lace use for the jewel box
Explanation:
\(\frac{4}{5}\) x \(\frac{5}{6}\) = \(\frac{20}{30}\) = \(\frac{2}{3}\)
\(\frac{5}{6}\) – \(\frac{2}{3}\) = \(\frac{5-4}{6}\) = \(\frac{1}{6}\)

Solve. Show your work.

Question 3.
Tasha finished a job in \(\frac{3}{4}\) hour. Megan finished it in of the time Tasha took. How long did Megan take to finish the job?
Answer:
45 minutes
Explanation:
Tasha finished a job in \(\frac{3}{4}\) hour.
Megan finished it in of the time Tasha took.
\(\frac{3}{4}\) x 60 = 45 minutes
45 minutes Megan take to finish the job

Question 4.
Lily has a bottle containing \(\frac{7}{8}\) quart of milk. She pours \(\frac{4}{5}\) of it into a bowl. What amount of milk does she pour into the bowl?
Answer:
\(\frac{7}{10}\)
Explanation:
Lily has a bottle containing \(\frac{7}{8}\) quart of milk.
She pours \(\frac{4}{5}\) of it into a bowl.
\(\frac{7}{8}\) x \(\frac{4}{5}\)
= \(\frac{28}{40}\)
= \(\frac{7}{10}\)
\(\frac{7}{10}\) amount of milk that she pour into the bowl

Question 5.
Raoul ran \(\frac{3}{4}\) mile in a race. Eduardo ran \(\frac{2}{7}\) of the distance that Raoul ran. What distance did Eduardo run?
Answer:
\(\frac{3}{14}\)
Explanation:
Raoul ran \(\frac{3}{4}\) mile in a race.
Eduardo ran \(\frac{2}{7}\) of the distance that Raoul ran.
\(\frac{3}{4}\) x \(\frac{2}{7}\)
= \(\frac{6}{28}\)
= \(\frac{3}{14}\)
\(\frac{3}{14}\) that Eduardo run

Solve. Draw models to help you.

Question 6.
Jenny spends \(\frac{1}{6}\) of her paycheck and saves \(\frac{2}{5}\) of the remaining amount. What fraction of her total paycheck is saved?
Answer:
\(\frac{1}{3}\)
Explanation
Jenny spends \(\frac{1}{6}\) of her paycheck
and saves \(\frac{2}{5}\) of the remaining amount.
x – \(\frac{1}{6}\)x
= \(\frac{5x}{6}\) pennies
\(\frac{5x}{6}\) x \(\frac{2}{5}\)
x = \(\frac{10}{30}\)
= \(\frac{1}{3}\)
\(\frac{1}{3}\) of her total paycheck is saved

Question 7.
In Rod’s family, \(\frac{3}{4}\) of the members wear glasses. Of those who do not wear glasses, \(\frac{1}{3}\) are male. What fraction of the family are males who do not wear glasses?
Answer:
\(\frac{1}{12}\)
Explanation:
In Rod’s family, \(\frac{3}{4}\) of the members wear glasses.
Of those who do not wear glasses, \(\frac{1}{3}\) are male.
x – \(\frac{3}{4}\)x
= \(\frac{4x-3x}{4}\)
= \(\frac{1}{4}\)x
x = \(\frac{1}{4}\) not wear glass
\(\frac{1}{4}\) x \(\frac{1}{3}\)
= \(\frac{1}{12}\)
\(\frac{1}{12}\) fraction of the family are males that not wear glasses

Solve. Draw models to help you.

Question 8.
Ned folded a set of origami figures. Of this set, \(\frac{5}{8}\) are cranes and \(\frac{1}{6}\) of the remainder are frogs. The rest are grasshoppers. What fraction of the origami figures are grasshoppers?
Answer:
\(\frac{11}{16}\)
Explanation:
Ned folded a set of origami figures. Of this set, \(\frac{5}{8}\) are cranes
and \(\frac{1}{6}\) of the remainder are frogs. The rest are grasshoppers.
\(\frac{5}{8}\) are cranes
\(\frac{3}{8}\) are not cranes
\(\frac{1}{6}\) x \(\frac{3}{8}\) = \(\frac{3}{48}\) = \(\frac{1}{16}\)
Let us convert
\(\frac{5}{8}\) as \(\frac{10}{16}\)
\(\frac{10}{16}\) + \(\frac{1}{16}\)
= \(\frac{11}{16}\)
\(\frac{11}{16}\) fraction of the origami figures are grasshoppers

Solve. Show your work

Question 9.
In a garden, \(\frac{2}{3}\) of the flowers are roses. Of the roses in the garden, \(\frac{5}{12}\) are yellow and the rest are red. What fraction of the flowers are red roses?
Answer:
\(\frac{1}{9}\)
Explanation:
In a garden, \(\frac{2}{3}\) of the flowers are roses.
Of the roses in the garden, \(\frac{5}{12}\) are yellow and the rest are red.
Roses = \(\frac{2}{3}\)
Yellow = \(\frac{5}{12}\) x \(\frac{2}{3}\)
= \(\frac{10}{36}\)
= \(\frac{5}{18}\)
Red = \(\frac{2}{3}\) – \(\frac{5}{18}\)
= \(\frac{36-30}{54}\)
= \(\frac{1}{9}\)
\(\frac{1}{9}\) fraction of the flowers are red roses

Question 10.
Karen collects local and foreign coins. Of the coins in her collection, \(\frac{1}{4}\) are foreign coins. Of the foreign coins, \(\frac{2}{5}\) are from Mexico. What fraction of the collection are foreign coins that are not from Mexico?
Answer:
\(\frac{3}{20}\) fraction of the collection are foreign coins that are not from Mexico
Explanation:
\(\frac{1}{4}\) are foreign coins
\(\frac{2}{5}\) x \(\frac{1}{4}\)
Mexico = \(\frac{1}{10}\)
Non Mexican
= \(\frac{1}{4}\)  – \(\frac{1}{10}\)
= \(\frac{5-2}{20}\)
= \(\frac{3}{20}\)

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 4 Practice 5 Real-World Problems: Multiplying Mixed Numbers to finish your assignments.

Math in Focus Grade 5 Chapter 4 Practice 5 Answer Key Real-World Problems: Multiplying Mixed Numbers

Solve. Show your work.

Question 1.
At a party, there are 8 guests. Each guest eats 2\(\frac{1}{4}\) oranges.
How many oranges do the 8 guests eat?
1 guest → 2\(\frac{1}{4}\) oranges
8 guests → ___ × ____ oranges
= _____
The 8 guests eat a total of ___ oranges.
Answer:
The 8 guests eat a total of 18
oranges.
Explanation:
1 guest → 2\(\frac{1}{4}\) oranges
8 guests → 8 × \(\frac{9}{4}\)  oranges
= 18

Question 2.
One pound of chicken costs $3. Jim buys 8\(\frac{2}{3}\) pounds of chicken. How much does Jim pay for the chicken?
Answer:
One pound of chicken  = $3
8\(\frac{2}{3}\) x 3
Explanation:

Question 3.
Nolan practices the piano for 1\(\frac{2}{5}\) hours every Saturday and Sunday. How long does he practice each weekend? Express your answer in hours and minutes.
Answer:
he practiced 2 hours 48 minutes
Explanation:
1\(\frac{2}{5}\) hours on Saturday
1\(\frac{2}{5}\) hours on Sunday
1\(\frac{2}{5}\) + 1\(\frac{2}{5}\)
2\(\frac{4}{5}\)
1 hour = 60 minutes
5 parts of 60 = 5 x 12 = 60
60 – 12 = 48
so, he practiced 2 hours 48 minutes

Solve. Show your work

Question 4.
Sue buys 5 pieces of fabric. Each piece of fabric is 1\(\frac{7}{10}\) yards long.
a. What is the total length of the fabric she buys?
Answer:
Sue buys 5 pieces of fabric.
Each piece of fabric is 1\(\frac{7}{10}\) yards long.

b. One yard of the fabric costs $5. How much does she pay for all 5 pieces of fabric?
Answer:
One yard of the fabric costs $5.
she pay for all 5 pieces of fabric
5 x 5 = 25
She paid $25

Question 5.
Angela works 1\(\frac{1}{2}\) hours a day and is paid $7 per hour. She works 5 days a week. How much does Angela earn in 7 weeks?
Answer:
Angela works 1\(\frac{1}{2}\) hours a day and is paid $7 per hour.
1\(\frac{1}{2}\) x 7

She works 5 days a week.
5 x 10\(\frac{1}{2}\)
= 50\(\frac{5}{2}\)
= 52\(\frac{1}{2}\)
Angela earn in 7 weeks
7 x 52\(\frac{1}{2}\)

Explanation:
7 x 5 = 35
35 x 7 = 245
245 x 1\(\frac{1}{2}\)
367\(\frac{1}{2}\)

This handy Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 11 to 13 provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Cumulative Review Chapters 11 to 13 Answer Key

Concepts and Skills

• Angles next to each other sum up to 180°

• Opposite angles are equal.

The double bar graph shows the number of pairs of black jeans and blue jeans produced in a factory in three days.

Complete. Use the data in the graph on page 145. (Lesson 11.1)

Question 1.
On day 2, ___ more pairs of blue jeans thon black jeans are produced.
Answer: 35.
Explanation:
On day 2, 35 more pairs of blue jeans than black jeans are produced.
80 – 45 = 35

Question 2.
On day ___ and day ___, the same number of pairs of black jeans are produced.
Answer:
Day 1 and 2
Explanation:
On day 1 and day 2 , the same number of pairs of black jeans are produced.

Question 3.
The greatest number of blue jeans is produced on day ____.
Answer:
Day 2
Explanation:
The greatest number of blue jeans is produced on day 2.
That is 80

Question 4.
On day 1, the difference between the number of pairs of blue jeans and black jeans produced is ___.
Answer: 15
Explanation:
On day 1, the difference between the number of pairs of blue jeans and black jeans produced is 15.
60 – 45 = 15

Question 5.
The total number of pairs of jeans produced in the three days is ___.
Answer: 350
Explanation:
The total number of pairs of jeans produced in the three days is 350.
60 + 45 = 105
80 + 45 = 125
35 + 85 = 120
105 + 125 + 120 = 350

Question 6.
The ratio of the number of pairs of block jeans produced to the number of pairs of blue jeans produced on day 3 is ____.
Answer: 17 : 7
Explanation:
The ratio of the number of pairs of block jeans produced to the number of pairs of blue jeans produced on day 3 is 17 : 7.
85 : 35 = 17 : 7

Question 7.
Express the number of black jeans produced on doy 1 as a fraction of the number of blue jeans produced on day 1. ___________
Answer: \(\frac{4}{3}\)
Explanation:
The number of black jeans produced on doy 1 as a fraction of the number of blue jeans produced on day 1. \(\frac{4}{3}\)
60 ÷ 45 = \(\frac{4}{3}\)

Question 8.
Express the total number of blue jeans produced as a percent of the total number of jeans produced in the three days. ____
Answer:
The total number of blue jeans produced as a percent of the total number of jeans produced in the three days. \(\frac{1}{2}\)
Explanation:
60 + 80 + 35 = 175
total number of jeans produced in the three days. = 350
\(\frac{1}{2}\)

Each solid is cut vertically along the line shown. Identify the solid shapes that result.

Explanation:

Question 9.
What are the coordinates of point A? ____
Answer:
1 and 4
Explanation:
1 and 4 are the coordinates of point A

Question 10.
How many quarts of milk are in 12 cups? ____
Answer:
3 quarts
Explanation:
3  quarts of milk are in 12 cups

Question 11.
How many cups of milk are in 3\(\frac{1}{2}\) quarts of milk?
Answer:
3\(\frac{1}{2}\) = 15 quarts
Explanation:
3\(\frac{1}{2}\) = 15 quarts
15 quarts of milk

Question 12.
How many cups of milk are in 5 quarts of milk? ___
Answer:
5 = 20 quarts
Explanation:
20 cups of milk are in 5 quarts of milk

Make an organized list to find the number of combinations. (Lesson 11.3)

Barry’s Yogurt Shop sells frozen yogurt with a topping. A customer can pick one of three flavors: vanilla, strawberry, and blueberry. The customer can pick one of three toppings: nuts, raisins, and sprinkles.

Question 13.
List all the possible combinations of yogurt flavor and topping.

Answer: 9 possibilities
Explanation:

Find the number of combinations. (Lesson 11.3)
Question 14.
Brenda has 1 red, 1 green and 1 gold bracelet. She has 4 pairs of earrings: stud, hoop, button, and dangling. She wants to find all the combinations of 1 bracelet and 1 pair of earrings that she can wear.
Answer:
12
Explanation:
She can wear 12 combinations

Question 15.
Draw a tree diagram to show the possible combinations.
Answer:

Explanation:
Tree diagram is shown above for possible combinations
4 x 3 = 12

Question 16.
Find the number of combinations by multiplication.
____ × ____ = ____
There are ___ combinations.
Answer:
4 x 3 = 12
There are 12 combinations.

Complete. (Lesson 11.4)

A bag has 5 green toothbrushes and 7 yellow toothbrushes. Tim and Cathy each pick a toothbrush, and then return it to the bag. They do this for 20 times each. The table shows some of their results.

Question 17.
Complete the table.

Answer:

Question 18.
The theoretical probability of picking a yellow toothbrush is ____.
Answer:
The theoretical probability of picking a yellow toothbrush is 2

Question 19.
The experimental probability of picking a green toothbrush that Tim’s results show is ____________
Answer:
The experimental probability of picking a green toothbrush that Tim’s results show is 3

Find the unknown angle measures. (Lesso 12.1)

Question 20.
\(\overleftrightarrow{A B}\) is a line.

Answer:
∠AOD = 43°
Explanation:
∠AOD = 90°
∠AOC = 47°
90 – 47 = 43°

Question 21.
\(\overleftrightarrow{A B}\) is a line. The measures of ∠a, ∠b, and ∠c are equal.

Answer:
m∠a = 60°
m∠b = 60°
m∠c = 60°
Explanation:
∠AOD = 180°
180 ÷ 3 = 60°

Find the unknown angle measures. (Lesson 12.1 and 12.2)

Question 22.
\(\overleftrightarrow{A B}\) is a line.

Answer:
∠BOC = 148°
∠DOE = 66°
Explanation:
∠AOB = 180°
∠AOC = 32°
180 – 32 = 148°
∠AOD = 63°
∠BOE =51°
∠AOB =180°
63 + 51 = 114
180 – 114 = 66
∠DOE = 66°

Question 23.
\(\overleftrightarrow{A B}\) is a line.

Answer:
m∠AOC = 131°
m∠BOD = 98°
Explanation:
∠AOB = 180°
∠BOC = 49°
180 – 49 = 131°
∠AOD = 82°
∠AOB =180°
180 – 82 = 98
∠BOD = 98°

Question 24.

Answer: m∠s = 51°

Explanation:
Complete angle = 360°
So m∠s =  360° – 145 ° + 94 ° +70°= 51°

Question 25.

Answer:  m∠p + m∠q  =116°
Explanation:
Complete angle = 360°
So m∠p + m∠q  = 360° – 64° + 90° +90° =116°

Question 26.

Answer: 8°
Explanation:
m∠COD= 180°
m∠COA= 180° – 98° = 82°
if AB is line
m∠BOA = 180°
m∠BOE= 90°
m∠COA = 82°
m∠COE= 180° – 98° + 82° =8°

Question 27.

Answer: m∠AOB= 104°
Explanation:
m∠BOA + m∠AOC = 210°
m∠COB + m∠BOA= 254°
Complete angle =360°
m∠AOC= 360° – m∠COB + m∠BOA=360°- 254° =106°
m∠BOC= 360°-m∠BOA + m∠AOC  = 360°- 210° =150°
m∠AOB =  360°-m∠AOC + m∠BOC = 360° – 150° + 106° =104°

Find the unknown angle measures. (Lesson 13.3)

\(\overleftrightarrow{A B}\), \(\overleftrightarrow{C D}\) and \(\overleftrightarrow{E F}\) are lines.

Question 28.

Answer:
m∠a =54 °
m∠b =126 °
Explanation:
\(\overleftrightarrow{A B}\) is line, So m∠BOA = 180 ° then
m∠b = 180 ° – m∠AOC  = 180 ° – 54° =126 °
\(\overleftrightarrow{C D}\) is line, So m∠COD= 180 ° then
m∠a = 180 ° – m∠b = 180 ° – 126° =54 °

Question 29.

Answer:
m∠a= 180 ° – m∠DOB= 180 ° -82° = 98 °
m∠b=  m∠DOA= 82°
Explanation:
Intersecting lines create two pairs of vertical angles which are congruent.  Furthermore, intersecting lines create adjacent angles that are supplementary (sum to 180 degrees)
m∠COD= 180 °
m∠a= 180 ° – m∠DOB= 180 ° -82° = 98 °
Vertical angles are always congruent, which means that they are equal.
m∠b=  m∠DOA= 82°

Question 30.

m∠b = ___
m∠c = ___
m∠d = ___
m∠e = ___
m∠b + m∠d + m∠e
= ____
Answer:
m∠b = m∠EOA =38°
m∠c = 180 ° – m∠EOA +m∠COF = 180 ° – 38° +70° =72°
m∠d = m∠c =72°
m∠e = m∠COF =70°
m∠b + m∠d + m∠e = 180 °
Explanation:
Intersecting lines create two pairs of vertical angles which are congruent.  Vertical angles are always congruent, which means that they are equal. Furthermore, intersecting lines create adjacent angles that are supplementary (sum to 180 degrees)
m∠EOF= 180 °
m∠c = 180 ° – m∠EOA +m∠COF = 180 ° – 38° +70° =72°
m∠b = m∠EOA =38°
m∠c = 72°
m∠d = m∠c =72°
m∠e = m∠COF =70°
m∠b + m∠d + m∠e = 180 °

Question 31.

m∠a = ___
m∠b = ___
m∠c = ___
Answer:
m∠a = 90°
m∠b = 90°
m∠c = 45°
Explanation:
Intersecting lines create two pairs of vertical angles which are congruent.  Vertical angles are always congruent, which means that they are equal. Furthermore, intersecting lines create adjacent angles that are supplementary (sum to 180 degrees)
m∠a =  180 °  – m∠COA  = 180 °  – 90° = 90°
m∠b = 180 °  – m∠COA  = 180 °  – 90° = 90°
m∠DOB = 90°
m∠c  =m∠DOB  – 45° = 90°  – 45° = 45°

Find the unknown angle measures. Then classify triangle ABC as an acute, obtuse, or right triangle. (Lessons 13.1 to 13.3)

Question 32.

m∠a = ____
___ triangle
Answer:
m∠a = 118°
Obtuse triangle
Explanation:
The three interior angles of a triangle will always have a sum of 180°.
m∠a  =180 ° –  m∠ABC+ m∠DOB  = 180°- 37°  + 25 ° = 118°
An obtuse triangle is a triangle with one angle that is greater than 90 degrees.
118°>90°. So it is Obtuse triangle

Question 33.

m∠b = ____
___ triangle
Answer:
m∠b = 64°
Obtuse triangle

Explanation:
The three interior angles of a triangle will always have a sum of 180°.
m∠b  =180 ° –  m∠ACB+ m∠BAC= 180°- 95°  + 24° = 64°
An obtuse triangle is a triangle with one angle that is greater than 90 degrees.
118°>90°. So it is Obtuse triangle

Question 34.

m∠c = ____
___ triangle
Answer:
m∠c = 38°
right triangle
Explanation:
The three interior angles of a triangle will always have a sum of 180°.
m∠b  =180 ° –  m∠BAC+ m∠ABC= 180°- 52°  + 90° = 38°
A right triangle is a triangle with one 90 degree angle.
m∠ABC= 90°. So it is right triangle

Question 35.

m∠u = ____
m∠t = ____
___ triangle
Answer:
m∠u = 65°
m∠t = 35°
ABD is Obtuse  triangle
ABC is acute triangle
Explanation:
The three interior angles of a triangle will always have a sum of 180°.
m∠u  =180 ° –  m∠BAC+ m∠ABC= 180°- 55°  + 60° = 65°
m∠BAD+ m∠ABD + m∠ADB = 180°
m∠ABD= 180° – m∠BAD + m∠ADB
m∠ABD= 180° – 55° + 30 =95°
m∠t = m∠ABD – m∠ABC= 95°-60°=35°
An obtuse triangle is a triangle with one angle that is greater than 90 degrees.
m∠ABD = 95°. So it is Obtuse triangle

Question 36.

m∠a = ____
Answer:
m∠a =  58°
Explanation:
The three interior angles of a triangle will always have a sum of 180°. and
Remaining sum of two angles  = 180° – 64° =116°.
The isosceles triangle theorem further states that the angles opposite to each of the equal sides must also be equal.
So m∠a = 116° divide by 2 = 58°

Question 37.

m∠b = ____
Answer:
m∠b = 50°
Explanation:
The isosceles triangle theorem further states that the angles opposite to each of the equal sides must also be equal.
one angle is 65° so it is isosceles triangle then opposite angle also 65°
The three interior angles of a triangle will always have a sum of 180°. then
m∠b = 180° – 65° + 65°=50°

Question 38.
AB = BC = AD

Answer:
m∠w = 27°
Explanation:
in Triangle ABC
m∠BAC+ m∠BCA = 180° –  m∠ABC = 180 – 42 =138
The isosceles triangle theorem further states that the angles opposite to each of the equal sides must also be equal.
m∠BAC = m∠BCA =138 divide by 2 =69°
in Triangle ABD
m∠ABD= m∠ADB =42°
The isosceles triangle theorem further states that the angles opposite to each of the equal sides must also be equal.
So m∠BAD = 180 – 84 =96°
m∠w = 96° – 69° =27°

Question 39.

m∠x = ____
Answer: m∠x = 23°

Explanation:
m∠CEA= m∠BEA= 90°
in Triangle BEA
m∠ABE= 180  – m∠BAE+ m∠BEA= 180 – 37 +90° =  53°
m∠x  =m∠ABE  –  30° = 53- 30=23°

Find the unknown angle measures. (Lesson 13.3)

Question 40.

Answer:

Explanation:
m∠ABC= 90° given
Triangle ADB is equilateral triangle – All three sides are equal. All three angles are congruent and are equal to 60 degrees.
m∠ABD =  60°
m∠a= m∠ABC- m∠ABD=90- 60=30°

Question 41.
ZY = YX = XZ

Answer:

Explanation:
ZY = YX = XZ So Triangle XYZ is equilateral triangle – All three sides are equal. All three angles are congruent and are equal to 60 degrees.
So m∠ZXY= m∠XZY=  60°
So m∠WXZ = 60 – 22 = 38
m∠ p = 180 – 38 + 60 =82°

Measure the sides of the triangles in inches. Then fill in the blanks. (Lessons 13. 1 and 13.4)

Explanation:

Question 42.
AB is ___________ inches.
Answer:
AB is 3 inches.

Question 43.
BC is ___________ inches.
Answer:
BC is 5 inches.

Question 44.
AC is _________ inches.
Answer:
AC is 3 inches.

Question 45.
AB + BC > _______
Answer:
AB + BC
3 + 5 = 8
AB + BC > AC
AC = 3

Question 46.
AB + AC > ________
Answer:
AB + AC > BC
AB = 3
BC = 5
AC = 3
3 + 3 = 6
6 > 5

Question 47.
BC + AC > ________
Answer:
BC + AC >  AB
BC = 5
AC = 3
3 + 5 = 8
AB = 3
8 > 3

Question 48.
What kind of triangle is ABC? ____
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.

Find the unknown angle measures in each parallelogram. (Lesson 13.5)

Question 49.

m∠c = ___
m∠d = ___
m∠e = ___
Answer:
m∠c = 60 °
m∠d = 120°
m∠e = 60 °
Explanation:

Question 50.

m∠f = ___
Answer:

m∠f = 35°
Explanation:
Opposite angles are equal in Parallelogram  So m∠BCD = 86°
In Triangle BCD, m∠BCD = 86° and m∠BDC= 59°
m∠f= 180-86°+59 = 35°

Find the unknown angle measures in each rhombus. (Lesson 13.5)

Question 51.

m∠b = ___
m∠c = ___
Answer:
m∠b = 136°
m∠c = 44°
Explanation:
Opposite angles are equal in rhombus So m∠b = 136°
Sum of any two adjacent angles is 180°. So m∠b + m∠c = 180°
then  m∠c = 180° – m∠b = 180 -136 =44°

Question 52.

m∠d = ___
m∠e = ___
Answer:

m∠d = 49°
m∠e = 82°
Explanation:
In Rhombus, All sides are equal and, opposite sides are parallel to each other.

\(\overline{W X}\) = \(\overline{X Y}\)  = \(\overline{Y Z}\) =\(\overline{Z W}\)
So WXY is isosceles  triangle. So m∠XWY = m∠XYW = m∠d= 49°
Then m∠WXY = 180 – 49 + 49 =82°

In Rhombus, Opposite angles are equal.
m∠e= 82°

Find the unknown angle measures in each trapezoid. (Lesson 13.5)

Question 53.
In EFGH, \(\overline{E F}\) || \(\overline{H G}\).

m∠b = ___
m∠c = ___
Answer:
m∠b =134°
m∠c = 90°
Explanation:
A right trapezoid also called the right-angled trapezoid, has a pair of right angles.
So m∠c = 90°
m∠b = 360 – 90 + 90 +49 =134°

Question 54.
In PQRS, \(\overline{P S}\) || \(\overline{Q R}\).

m∠d = ___
Answer:
m∠d = 104°
Explanation:
In Triangle PQS,
m∠PQS =  180 – 104 +40 =76

In trapezoid, Angles next to each other sum up to 180°
m∠PSR = 180 -104 = 76°
m∠QSR = 76 -40= 36°
m∠QRS= 104
m∠d= 180 – 36 +40= 104°

Problem Solving

Solve. Show your work.

The graph shows a measurement in yards (x-axis) and its corresponding measurement in feet (y-axis).

Question 55.
The cost of 3 yards of fabric is $24. What is the cost of 36 feet of fabric?
Answer: $96
Explanation:
As per graph
3 yards and 9 feets = $24
So 36 feets= 12 yards
So 12yards price is 4 x $24 = $96

Solve. Show your work.

Question 56.
Each letter of the word JOURNAL is written on separate cards and put into a bag. First, one card is drawn. Then, the card is colored blue or yellow.

a. Draw a tree diagram to show the possible combinations of cards and colors.
Answer:

Explanation:
4 is colored blue
and 3 is colored red

b. What is the theoretical probability of picking a combination with a vowel?
Answer:
1 : 2 is the is the theoretical probability of picking a combination with a vowel

Solve. Show your work.

Question 57.
In the triangle ABC, AB = 4 centimeters, BC = 7 centimeters and AC is longer than 8 centimeters. If the length of \(\overline{A C}\) is in whole centimeters, what are the possible lengths of \(\overline{A C}\)?
Answer: AC = 9 or 10 centimeters
Explanation:
In a Triangle, sum of two sides should be greater than other side.
AC is longer than 8 centimeters. 4+ 7 is 11. so AC should not be longer than 11cm
4+7 > 9
4+9 > 7
7 + 9 > 4
or
4+7 > 10
4+10 > 7
7 + 10 > 4

Question 58.
ABCD is a trapezoid and ABED is a parallelogram. \(\overline{A B}\) || \(\overline{D C}\), \(\overline{A D}\) || \(\overline{B E}\), and BE = BC. Find the measure of ∠BCE.

Answer:
m∠BCE = 45°
Explanation:

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 3 Practice 2 Subtraction Without Regrouping to finish your assignments.

Math in Focus Grade 2 Chapter 3 Practice 2 Answer Key Subtraction Without Regrouping

Solve.
Show how to check your answer.

Example
Mr. Ong’s orchard has 175 trees. 152 trees grow fruit. How many trees do not grow fruit?
175 – 152 = 23

23 trees do not grow fruit.

Question 1.
Gina has 436 beads.
She uses 123 beads to make a necklace.
How many beads does she have left?

She has _________ beads left.
Answer:
She has 313 beads left.

Explanation:
Given that Gina has 436 beads and she uses 123 beads to make a necklace. So the number of beads does she have left is 436-123 which is 313 beads.

Question 2.
David’s book has 345 pages. He reads 231 pages of the book. How many pages does he have left to read?
He has ___ pages left to read.
Answer:
He has 114 pages left to read.

Explanation:
Given that David’s book has 345 pages and he reads 231 pages of the book. So the number of pages does he have left to read is 345-231 which is 114 pages.

Solve.
Show how to check your answer.

Question 3.
The lunchroom has 498 chairs. The janitor removes 211 chairs. How many chairs are left in the lunchroom?

___ chairs are left in the lunchroom.
Answer:
287 chairs are left in the lunchroom.

Explanation:
Given that the lunchroom has 498 chairs and the janitor removes 211 chairs. So the number of chairs are left in the lunchroom is 498-211 which is 287 chairs.

Question 4.
Last year, Kennedy School recycled 745 plastic bottles. This year, the school recycled 133 fewer plastic bottles than last year. How many plastic bottles did the school recycle this year?
Kennedy School recycled ___ plastic bottles this year.
Answer:
Kennedy School recycled 612 plastic bottles this year.

Explanation:
Given that Kennedy School recycled 745 plastic bottles last year and this year, the school recycled 133 fewer plastic bottles than last year. So the number of plastic bottles did the school recycle this year is 745-133 which is 612 plastic bottles.

Question 5.
A pilot made 347 flights last year. He made 124 fewer flights this year than last year. How many flights did the pilot make this year?

The pilot made ___ flights this year.
Answer:
The pilot made 223 flights this year.

Explanation:
Given that a pilot made 347 flights last year and he made 124 fewer flights this year than last year. So the number of flights did the pilot make this year is 347-124 which is 223 flights.

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 3 Practice 5 Subtraction with Regrouping in Hundreds and Tens to finish your assignments.

Math in Focus Grade 2 Chapter 3 Practice 5 Answer Key Subtraction with Regrouping in Hundreds and Tens

Regroup the hundreds and tens. Then subtract.

Question 1.

335 – 142 = ?
335 – 142
= 3 hundreds 3 tens 5 ones – 1 hundred 4 tens 2 ones
= 2 hundreds _________ tens 5 ones – 1 hundred 4 tens 2 ones
= ________ hundred ________ tens ________ ones
= ____
335 – 142 = _______
Use addition to check your answer.

Answer:
335 – 142 = 193,
193+142 = 335.

Explanation:
Given that 335 – 142 which is 193. So to check the answer, we will perform addition. So
193+142 = 335.
= 3 hundreds 3 tens 5 ones – 1 hundred 4 tens 2 ones
= 2 hundreds 13 tens 5 ones – 1 hundred 4 tens 2 ones
= 1 hundred 9 tens 3 ones
= 193
335 – 142 = 193.

Question 2.

Answer:
669 – 281 = 388,
388+281 = 669.

Explanation:
Given that 669 – 281 which is 388. So to check the answer, we will perform addition. So
388+281 = 669.

Question 3.

Answer:
714 – 363 = 351,
351+363 = 714.

Explanation:
Given that 714 – 363 which is 351. So to check the answer, we will perform addition. So
351+363 = 714.

Question 4.
765 – 695 = ___

Answer:
765 – 695 = 70,
695+70 = 765.

Explanation:
Given that 765 – 695 which is 70. So to check the answer, we will perform addition. So
695+70 = 765.

Question 5.
908 – 568 = ___

Answer:
908-568 = 340,
340+568 = 908.

Explanation:
Given that 908-568 which is 340. So to check the answer, we will perform addition. So
340+568 = 908.

Subtract.

Question 6.

Answer:

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 3 Practice 6 Subtraction with Regrouping in Hundreds and Tens to finish your assignments.

Math in Focus Grade 2 Chapter 3 Practice 6 Answer Key Subtraction with Regrouping in Hundreds and Tens

Solve.

Show how to check your answer.

Question 1.
A store has 519 model airplanes. It sells 228 model airplanes. How many model airplanes are left?
There are ___ model airplanes left.
Answer:
There are 231 model airplanes left.

Explanation:
Given that a store has 519 model airplanes and it sells 228 model airplanes. So the number of model airplanes left is 519-228 = 231 airplanes. So to check the answer, we will perform an addition which is 228+231 = 519.

Question 2.
A florist sells 755 roses in the morning. She sells 191 roses in the afternoon. How many fewer roses does she sell in the afternoon?

She sells ___ fewer roses in the afternoon.
Answer:
She sells 564 fewer roses in the afternoon.

Explanation:
Given that a florist sells 755 roses in the morning and she sells 191 roses in the afternoon. So the fewer roses does she sell in the afternoon is 755-191 which is 564 roses.

Question 3.
478 babies were born in August and September. 190 babies were born in August. How many babies were born in September?

____ babies were born in September.
Answer:
288 babies were born in September.

Explanation:
Given that 478 babies were born in August and September and 190 babies were born in August. So the number of babies were born in September is 478-190 which is 288 babies.

Solve.

Show how to check your answer.

Question 4.
Washington Elementary School has 883 students. 693 of the students go to the school baseball game. How many students do not go to the game?
_____ students do not go to the game.
Answer:
190 students do not go to the game.

Explanation:
Given that Washington Elementary School has 883 students and 693 of the students go to the school baseball game. So the number of students who do not go to the game is 883-693 which is 190 students.

Question 5.
366 beads are in a box. 195 of the beads are green. How many of the beads are not green?
____ of the beads are not green.
Answer:
171 of the beads are not green.

Explanation:
Given that 366 beads are in a box and 195 of the beads are green. So the number of beads is not green is 366-195 which is 171 beads.

Question 6.
Mario has 534 kites at his shop. He sells 452 of the kites in a week. How many kites does Mario have left?
Mario has ___ kites left.

Answer:
Mario has 82 kites left.

Explanation:
Given that Mario has 534 kites at his shop and he sells 452 of the kites in a week. So the number of kites does Mario has left is 534-452 which is 82 kites.

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 4 Practice 3 Comparing Two Sets to finish your assignments.

Math in Focus Grade 2 Chapter 4 Practice 3 Answer Key Comparing Two Sets

Solve.
Complete the bar models to help you.

Question 1.
102 children at a swimming pool do not wear goggles. 23 more children wear goggles than those who do not wear goggles. How many children wear goggles?

______ children wear goggles.
Answer:
125 children wear goggles.

Explanation:
Given that 102 children at a swimming pool do not wear goggles and 23 more children wear goggles than those who do not wear goggles. So the total number of children wearing goggles is 102+23 which is 125 children.

Question 2.
Alice made 166 ham sandwiches for a party. She made 77 fewer cheese sandwiches than ham sandwiches for the party. How many cheese sandwiches did Alice make?

Alice made ___ cheese sandwiches.
Answer:
Alice made 89 cheese sandwiches.

Explanation:
Given that Alice made 166 ham sandwiches for a party and she made 77 fewer cheese sandwiches than ham sandwiches which are 166-77 = 89 cheese sandwiches.

Solve.

Draw bar models to help you.

Question 3.
Sam makes 123 party favors. Lily makes 87 more party favors than Sam. How many party favors does Lily make?
Lily makes ___ party favors.
Answer:
Lily makes 210 party favors.

Explanation:
Given that Sam makes 123 party favors and Lily makes 87 more party favors than Sam which is 123+87 = 210 party favors.

Question 4.
952 children watch a funny movie. 265 fewer adults than children watch the funny movie. How many adults watch the funny movie?
____ adults watch the funny movie.
Answer:
687 adults watch the funny movie.

Explanation:
Given that 952 children watch a funny movie and 265 fewer adults than children watch a funny movie. So the adults watching the funny movie is 952-265 which is 687.

Solve.

Complete the bar models to help you.

Question 5.
Mr. Diaz has 347 apple trees in his orchard. He has 162 more apple trees than peach trees in his orchard. How many peach trees does Mr. Diaz have in his orchard?

Mr. Diaz has ___ peach trees in his orchard.
Answer:
Mr. Diaz has 185 peach trees in his orchard.

Explanation:
Given that Mr. Diaz has 347 apple trees in his orchard and he has 162 more apple trees than peach trees in his orchard. So let the peach trees be X as 162 more apple trees than peach trees, so
X+162 = 347,
X = 347-162
= 185 peach trees.

Question 6.
Shop A sells 97 television sets in December. It sells 166 fewer television sets than Shop B in December. How many television sets does Shop B sell in December?

Shop B sells _________ television sets in December.
Answer:

Solve.

Draw bar models to help you.

Question 7.
The school cook orders 219 hamburgers. He orders 120 more hamburgers than hot dogs. How many hot dogs does the school cook order?

The school cook orders ____ hot dogs.
Answer:
The school cook orders 99 hot dogs.

Explanation:
Given that the school cook orders 219 hamburgers and he orders 120 more hamburgers than hot dogs. So the number of hot dogs does the school cook order is
X+120 = 219
X = 219-120
= 99.

Question 8.
234 flag twirlers march in the Fourth of July parade. There are 159 fewer flag twirlers than band members at the parade. How many band members are at the parade?
____ band members are at the parade.
Answer:
The number of band members are at the parade is 75.

Explanation:
Given that 234 flag twirlers march in the Fourth of July parade and there are 159 fewer flag twirlers than band members at the parade, so the number of band members are at the parade is
X-159 = 234
X = 234-159
= 75.

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 4 Using Bar Models: Addition and Subtraction to finish your assignments.

Math in Focus Grade 2 Chapter 4 Answer Key Using Bar Models: Addition and Subtraction

Math Journal

Write an addition story or a subtraction story for each bar model. Then solve.

Question 1.

Answer:
The total number of stickers did Ben collected in all is 52.

Explanation:

Given that Ben collected 36 stickers on Monday and 16 stickers on Tuesday. So the total number of stickers did Ben collected in all is 36+16 which is 52.

Question 2.

Answer:
The total number of pages did Emma had now is 19 pages.

Explanation:

Given that Emma has 63 pages and she gave 44 pages to her friend. So the total number of pages did Emma had now is 63-44 which is 19 pages.

Write an addition story or a subtraction story for the bar model. Then solve.

Question 3.

Answer:

Put On Your Thinking Cap!

Problem Solving

Solve.

Question 1.
Sean has 24 fewer toys than Winona. After Winona gives some toys to Sean, both of them have the same number of toys. How many toys does Winona give Sean? Winona gives Sean ___ toys.
Answer:
Winona gives Sean 12 toys.

Explanation:
Given that Sean has 24 fewer toys than Winona. As Winona gives some toys to Sean and both of them have the same number of toys. Here, Winona’s toy count decreases by 12 and Sean’s increases by 12 and the original difference of 24 disappears. So Winona must give Sean half the difference, so there are 12 toys.

Question 2.
Nadia has 20 more postcards than Pete. After Nadia gives Pete some postcards, Pete has 2 more postcards than Nadia. How many postcards does Nadia give to Pete?
Nadia gives Pete ___ postcards.
Answer:

Chapter Review/Test

Vocabulary

Fill in the blanks.

Use the words in the box.

Question 1.
In this model, you ___ two ___ of data.
Answer:
In this model, you compare two sets of data.

Question 2.
To find how many more apricots there are than peaches, you ____
Answer:
To find how many more apricots there are than peaches, you subtract.

Question 3.
To find the total number of apricots and peaches, you ___
Answer:
To find the total number of apricots and peaches, you add

Concepts and Skills

Fill in each with + or -. Then fill in the blanks.

Question 4.

Answer:
38+21 = 59.

Explanation:
Here, we have performed addition to the given numbers.

Question 5.

Answer:
50-38 = 12.

Explanation:
Here, we have performed subtraction to the given numbers.

Question 6.

Answer:
45+12 = 57.

Explanation:
Here, we have performed addition to the given numbers.

Question 7.

Answer:
78-52 = 26.

Explanation:
Here, we have performed subtraction to the given numbers.

Problem Solving

Solve.

Draw bar models to help you.

Question 8.
A jewelry store has 198 rings and bracelets altogether. It has 89 bracelets. How many more rings than bracelets does the store have?
The store has ___ more rings than bracelets.
Answer:
The store has 109 more rings than bracelets.

Explanation:
Given that a jewelry store has 198 rings and bracelets altogether and it has 89 bracelets. So the number of rings than bracelets does the store have is 198-89 which is 109 rings.

Question 9.
Andy reads 56 more pages of his book on Monday than on Tuesday. He reads 125 pages on Monday. How many pages in all does he read on Monday and Tuesday?
He reads ___ pages in all.
Answer:
He reads 181 pages in all.

Explanation:
Given that Andy reads 56 more pages of his book on Monday than on Tuesday and he reads 125 pages on Monday. So the number of pages in all does he read on Monday and Tuesday is 125+56 which is 181 pages.

Question 10.
An office has 223 workers. 132 of the workers are men. How many more men work in the office than women?
____ more men work in the office than women.
Answer:
41 more men work in the office than women.

Explanation:
Given that an office has 223 workers and in that 132 of the workers are men. So the number of women is 223-132 which is 91 women. And the number of men more than women is 132-91 which is 41.

Question 11.
A furniture shop has 581 tables and chairs in all. There are 125 tables. How many more chairs than tables are there in the shop?
There are ____ more chairs than tables in the shop.
Answer:
There are 331 more chairs than tables in the shop.

Explanation:
Given that a furniture shop has 581 tables and chairs in all and there are 125 tables. As the total number of tables and chairs is 581, so
125+c = 581
c = 581-125
= 456 chairs.
So the number of more chairs than tables in the shop is 456-125 which is 331 more chairs.

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 1 Practice 3 Comparing Numbers to finish your assignments.

Math in Focus Grade 2 Chapter 1 Practice 3 Answer Key Comparing Numbers

Write greater than or less than in the blanks.

Example

First compare the hundreds. If the hundreds are the same, compare the tens. If the tens are the same, compare the ones.

Question 1.

Answer:

Explanation:
First compared the hundreds.
As the hundreds are the same, compared the tens.
181 > 118

Question 2.

Answer:

Explanation:
Compared the hundreds as the hundreds are different
959 > 595

Compare.
Write > or < in the .

Example

Write > or < in the .

Question 3.

Answer:

Explanation:
thousands are greater than hundreds

Question 4.

Answer:

Explanation:
compared the hundreds as the hundreds are different
897 > 789

Question 5.
Write T for true or F for false.
55 is less than 455. ____
355 is greater than 455. _______
400 is less than 455. ______
450 is greater than 405. ______
800 < 809 ______
980 < 809 ____
89 > 98 ____
863 > 862 ____
Answer:
55 is less than 455.  T
55 < 455
355 is greater than 455. F
355 < 455
400 is less than 455. T
400 < 455
450 is greater than 405. T
450 > 405
800 < 809 T
800 is less than 809
980 < 809 F
980 is greater than 809
89 > 98 F
89 is lesser than 98
863 > 862 T
863 is greater than 862

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Mid Year Review to score better marks in the exam.

Math in Focus Grade 4 Mid Year Review Answer Key

Multiple Choice
Fill in the circle next to the correct answer.
Question 1.
13 thousands + 4 tens + 8 ones in standard form is ___ (Lesson 1.1)
(A) 1,348
(B) 10,348
(C) 13,048
(D) 13,480
Answer:
13 thousands + 4 tens + 8 ones in standard form = 13048.
(C) 13,048.

Explanation:
13 thousands + 4 tens + 8 ones in standard form = 13000 + 40 + 8
= 13040 + 8
= 13048.

Question 2.
In the number 83.415 the value of the digit 3 is ____. (Lesson 1.1)
(A) 30
(B) 300
(C) 3,000
(D) 30,000
Answer:
In the number 83.415, the value of the digit 3 is 3000.
(C) 3,000

Explanation:
In the number 83.415,
8 tens 3 ones 4 tenths 1 hundredths 5 thousandths.
the value of the digit 3 is 3000.

Question 3.
1.000 more than 37,568 is ____ (Lesson 1.2)
(A) 36,568
(B) 37,468
(C) 37,668
(D) 38,568
Answer:
1.000 more than 37,568 = 38,568.
(D) 38,568.

Explanation:
1.000 more than 37,568 = 37,568 + 1000 = 38,568.

Question 4.
Estimate 681 – 307 by rounding to the nearest 100. (Lesson 2.1)
(A) 300
(B) 370
(C) 374
(D) 400
Answer:
Estimate 681 – 307 by rounding to the nearest 100 = 400.
(D) 400

Explanation:
Estimate 681 – 307 by rounding to the nearest 100:
681 nearest hundred = 700.
307 nearest hundred = 300.
Difference 681 – 307 = 700 – 300 = 400.

Question 5.
Which is the greatest common factor of 27 and 45? (Lesson 2.2)
(A) 1
(B) 3
(C) 9
(D) 45
Answer:
Greatest common factor of 27 and 45 = 9.
(C) 9.

Explanation:
Greatest common factor of 27 and 45 = 9.
3 × 9 = 27.
5 × 9 = 45.

Question 6.
Which pair of numbers has both a prime and a composite number? (Lesson 2.2)
(A) 4 and 7
(B) 3 and 13
(C) 14 and 28
(D) 6 and 8
Answer:
Pair of numbers has both a prime and a composite number: 3 and 13.
(B) 3 and 13.

Explanation:
A prime number is a whole number greater than 1. It has exactly two factors, that is, 1 and the number itself.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.
Pair of numbers has both a prime and a composite number:
A. 4 and 7 = (2 × 2) and (1 × 7)
B. 3 and 13 = (1 × 3) and (1 × 13)
C. 14 and 18 = [(2 × 7) (1 × 7)] and  [(2 × 9) (3 × 3)]
D. 6 and 8 = [(2 × 3) (1 × 6)] and [(2 × 4) (1 × 8)]

Question 7.
What is the sum of the first two multiples of 6? (Lesson 2.3)
(A) 3
(B) 6
(C) 12
(D) 18
Answer:
Sum of the first two multiples of 6: 18.
(D) 18.

Explanation:
Sum of the first two multiples of 6:
6 × 1 = 6.
2 × 6 = 12.
Sum = 6 + 12 = 18.

Question 8.
Mr. Finch exercises at the gym every two days. Mr. Chavez exercises at the gym every five days. When will they meet next if they first met on January 5? (Lesson 2.3)
(A) January 7
(B) January 10
©) January 15
(D) January 25
Answer:
Next day when they meet = (2 × 5) = January 10.
(B) January 10.

Explanation:
Number of days Mr. Finch exercises at the gym = every 2.
Number of days Mr. Chavez  exercises at the gym = every 5.
Next day when they meet = (2 × 5) = January 10.

Question 9.
Divide 5,61 3 by 7. The remainder is ____ (Lesson 3.4)
(A) 1
(B) 6
(C) 18
(D) 81
Answer:
Divide 5,61 3 by 7. The remainder is 6.
(B) 6.

Explanation:
5613 ÷ 7 = 801 \(\frac{6}{7}\)

Question 10.
After using 35 jars to store 14 marbles each, Ali has 3 marbles left. How many marbles did he have at first? (Lesson 3.5)
(A) 52
(B) 178
(C) 490
(D) 493
Answer:
Number of marbles Alia has first = 493.
(D) 493.

Explanation:
Number of jars store using = 35.
Number of marbles each jar has = 14.
Number of marbles left = 3.
Number of marbles Alia has first = (Number of jars store using × Number of marbles each jar has) + Number of marbles left
= (35 × 14) + 3
= 490 + 3
= 493.

Question 11.
The table shows the medals different teams won at a competition. (Lesson 4.2)

At which intersection was one medal won?
(A) Sandcastle and Gold
(B) Coral Reef and Silver
(C) Sunshine and Bronze
(D) Seahorse and Silver
Answer:
Intersection one medal won = Coral Reef and Silver.
(B) Coral Reef and Silver.

Explanation:
Intersection one medal won = Coral Reef and Silver.

Question 12.
Find the mode. (Lesson 5.2)
31 lb 36 lb 21 lb 40 lb 38 lb 40 lb
(A) 31 lb
(B) 36 lb
(C) 37 lb
(D) 40 lb
Answer:
Mode of 31 lb 36 lb 21 lb 40 lb 38 lb 40 lb = 40lb.
(D) 40 lb.

Explanation:
Mode:
31 lb 36 lb 21 lb 40 lb 38 lb 40 lb
31 = 1.
36 = 1.
21 = 1.
40 = 2.
38 = 1.

Question 13.
Jim ordered cons of fruit cocktail for his diner for 6 months. (Lesson 5.3)

What is the median number of cans he ordered?
(A) 29 cans
(B) 32 cans
(C) 33 cans
(D) 40 cans
Answer:
Median number of cans he ordered = 33 cans.

Explanation:
Median is the middle number in a sorted list of numbers. To determine the median value in a sequence of numbers, the numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest.
0 1 3 3 6 9
Median number of cans he ordered = 33 cans.

Question 15.
Stacy draws one of these number cards from a bag.

What is the probability that she draws a number less than 10? (Lesson 5.5)
(A) \(\frac{1}{2}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{2}{3}\)
(D) \(\frac{1}{6}\)
Answer:
Probability that she draws a number less than 10 = \(\frac{1}{6}\)
(D) \(\frac{1}{6}\)

Explanation:
Probability is simply how likely something is to happen. Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Probability that she draws a number less than 10 = card less than 10 ÷ total number of cards.
= 1 ÷ 6 or \(\frac{1}{6}\).

Question 16.
Which two fractions have a sum of \(\frac{9}{10}\)? (Lesson 6.1)
(A) \(\frac{1}{2}\) and \(\frac{4}{10}\)
(B) \(\frac{1}{2}\) and \(\frac{1}{10}\)
(C) \(\frac{2}{5}\) and \(\frac{1}{10}\)
(D) \(\frac{3}{4}\) and \(\frac{6}{6}\)
Answer:
Two fractions have a sum of \(\frac{9}{10}\) = (A)
(A) \(\frac{1}{2}\) and \(\frac{4}{10}\)

Explanation:
(A) \(\frac{1}{2}\) and \(\frac{4}{10}\)
Sum = 0.5 + 0.4 = 0.9.
(B) \(\frac{1}{2}\) and \(\frac{1}{10}\)
Sum = 0.5 + 0.1 = 0.6.
(C) \(\frac{2}{5}\) and \(\frac{1}{10}\)
Sum = 0.4 + 0.1 = 0.5.
(D) \(\frac{3}{4}\) and \(\frac{6}{6}\)
Sum = 0.75 + 1 = 1.75.

Question 17.
Which mixed number is represented by A on the number line? (Lesson 6.3)

(A) 3\(\frac{4}{5}\)
(B) 3\(\frac{2}{3}\)
(C) 4\(\frac{1}{3}\)
(D) 4\(\frac{2}{3}\)
Answer:
A = 3.8.
(A) 3\(\frac{4}{5}\).

Explanation:
(A) 3\(\frac{4}{5}\) = (15 + 4) ÷ 5 = \(\frac{19}{5}\) = 3.8.
(B) 3\(\frac{2}{3}\) = (9 + 2) ÷ 3 = \(\frac{11}{3}\) = 3.67.
(C) 4\(\frac{1}{3}\) = (12 + 1) ÷ 3 = \(\frac{13}{3}\) = 4.33.
(D) 4\(\frac{2}{3}\) = (12 + 2) ÷ 3 = \(\frac{14}{3}\) = 4.67.

Question 18.
How many fifths are in 2\(\frac{3}{5}\) ? (Lesson 6.4)
(A) 10
(B) 11
(C) 13
(D) 23
Answer:
13 fifths are in 2\(\frac{3}{5}\).
(C) 13.

Explanation:
2\(\frac{3}{5}\) = (10 + 3) ÷ 5 = \(\frac{13}{5}\)

Question 19.
Express \(\frac{14}{6}\) as a mixed number in simplest form. (Lesson 65)
(A) 1\(\frac{4}{6}\)
(B) 1\(\frac{2}{3}\)
(C) 2\(\frac{2}{6}\)
(D) 2\(\frac{1}{3}\)
Answer:
Simplest form of \(\frac{14}{6}\) = 2\(\frac{2}{6}\)
(C) 2\(\frac{2}{6}\)

Explanation:
Simplest form of \(\frac{14}{6}\) = 2\(\frac{2}{6}\)

Question 20.
Ms. Lee cut a piece of yarn into different fractional parts:
\(\frac{1}{12}\), \(\frac{1}{4}\) and \(\frac{5}{12}\). What fraction of the yarn is left? (Lesson 6.7)
(A) \(\frac{1}{4}\)
(B) \(\frac{5}{12}\)
(C) \(\frac{8}{12}\)
(D) \(\frac{3}{4}\)
Answer:
Fraction of the yarn is left = \(\frac{1}{4}\).
(A) \(\frac{1}{4}\)

Explanation:
\(\frac{1}{12}\), \(\frac{1}{4}\) and \(\frac{5}{12}\).
Fraction of the yarn is left = 1 – (\(\frac{1}{12}\) +  \(\frac{1}{4}\) + \(\frac{5}{12}\))
= 1 – (0.08 + 0.25 + 0.42)
= 1 – (0.33 + 0.42)
= 1 – 0.75
= 0.2 or\(\frac{1}{4}\)

Short Answer
Read each question carefully. Write your answer in the space provided. Give your answers in the correct units.
Question 21.
Write forty thousand, sixteen in expanded form. (Lesson 1.1)
Answer:
Expanded form of forty thousand, sixteen = 40,016.

Explanation:
Expanded form of forty thousand, sixteen = 40,000 + 16 = 40,016.

Question 22.
Arrange the numbers in order from least to greatest. (Lesson 1.2)

Answer:

Explanation:
Numbers in order from least to greatest :
6,047, 6,407, 19,999, 20,005.

Question 23.
Estimate the quotient of 713 ÷ 9. (Lesson 2.1)
____
Answer:
Quotient of 713 ÷ 9 = 79.

Explanation:
Quotient of 713 ÷ 9 = 79\(\frac{2}{9}\).

Question 24.
The table shows the number of people who visited the space ride at a theme park. Complete the table. (Lesson 4.2)

Answer:

Explanation:
Number of male who visited the space ride at a theme park = 18.
Total adults who visited the space ride at a theme park = 50.
Number of female who visited the space ride at a theme park = Total adults who visited the space ride at a theme park – Number of male who visited the space ride at a theme park
= 50 – 18
= 32.
Number of male children who visited the space ride at a theme park = 32.
Number of female children who visited the space ride at a theme park = 38.
Total number of children who visited the space ride at a theme park = Number of male children who visited the space ride at a theme park + Number of female children who visited the space ride at a theme park
= 32 + 38
= 70.

Use the table to answer Exercises 25 and 26.
Question 25.
How many people visited the space ride? (Lesson 4.2) ____
Answer:
Total number of people who visited the space ride at a theme park = 120.

Explanation:
Total adults who visited the space ride at a theme park = 50.
Total number of children who visited the space ride at a theme park = 70.
Total number of people who visited the space ride at a theme park = Total adults who visited the space ride at a theme park + Total number of children who visited the space ride at a theme park
= 50 + 70
= 120.

Question 26.
What fraction of the people who visited the space ride were children? (Lesson 6.7) _____
Answer:
Fraction of the people who visited the space ride were children = 7 ÷ 12 or \(\frac{7}{12}\).

Explanation:
Total number of children who visited the space ride at a theme park = 70.
Total number of people who visited the space ride at a theme park = 120.
Fraction of the people who visited the space ride were children = Total number of children who visited the space ride at a theme park ÷ Total number of people who visited the space ride at a theme park
= 70 ÷ 120
= 7 ÷ 12 or \(\frac{7}{12}\).

The line graph shows the number of visitors at a museum during the course of a day. (Lesson 4.3)

Question 27.
By how much did the visitor population increase from 1:00 P.M. to 3:00 P.M.? ______________
Answer:
35 visitor population increased from 1:00 P.M. to 3:00 P.M.

Explanation:
Visitor Population at 1:00 P.M = 45.
Visitor Population at 3:00 P.M = 80.
Difference:
Visitor Population at 3:00 P.M – Visitor Population at 1:00 P.M
= 80 – 45
= 35.

Question 28.
During which interval did the visitor population decrease the most? ___
Answer:
5:00 P.M to 7:00 P.M interval did the visitor population decrease the most of 55.

Explanation:
Visitor Population at 9:00 A.M = 25.
Visitor Population at 11:00 A.M = 45.
Visitor Population at 1:00 P.M = 45.
Visitor Population at 3:00 P.M = 80.
Visitor Population at 5:00 P.M = 120.
Visitor Population at 7:00 P.M = 65.
Visitor Population at 9:00 P.M = 40.
5:00 P.M to 7:00 P.M interval
= Visitor Population at 5:00 P.M – Visitor Population at 7:00 P.M
= 120 – 65
= 55.

Question 29.
During which interval did the same number of visitors arrive and depart?
Answer:
11:00 A.M interval did the same number of visitors arrive and depart.

Explanation:
Visitor Population at 11:00 A.M = 45.
Visitor Population at 1:00 P.M = 45.

Use the line plot to solve Exercises 30 and 31. (Lesson 5.2)
The line plot shows the number of siblings each student in John’s class has.

Question 30.
Find the median of the set of data. ____
Answer:
Median of the set of data = 2.

Explanation:
Number of siblings = 0 1 2 3 4
Median of the set of data = 2.

Question 31.
Find the mode of the set of data. ____
Answer:
Mode of the set of data = 2.

Explanation:
The mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x (i.e, X = x) at which the probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.
Number of siblings in 2 are more.

Use the stem-and-leaf plot to solve Exercises 32 and 33. (Lesson 5.3)
The stem-and-leaf plot shows the number of orchids produced by 10 greenhouse plants in one month.

Question 32.
The median of the set of data is ___
Answer:
Median of the set of data = 5.

Explanation:
0 2 3 4 5 5 6 8 9 9
Median of the set of data = (5 + 5 ) ÷ 2
= 10 ÷ 2
= 5.

Question 33.
The outlier of the set of data is ___.
Answer:
The outlier of the set of data is 6.

Explanation:
Outliers are data points that don’t fit the pattern of rest of the numbers. They are the extremely high or extremely low values in the data set. A simple way to find an outlier is to examine the numbers in the data set.
8  9  5   5  6  0  2  3  4  9

Look at the spinner. Write more likely, less likely, equally likely, certain, or impossible. Explain your answer. (Lesson 5.4)

Question 34.
The spinner is ___ to land on an odd number or an even number.
Reason: ____
Answer:
The spinner is certain to land on an odd number.

Explanation:
The spinner is certain to land on an odd number because spinner hand is on 3 (odd number) not even number.

The bar graph shows the color of the horses at a horse show.

Question 35.
Which set is more likely to be the one shown in the bar graph? (Lesson 5.4)

Answer:
Set C is more likely to be the one shown in the bar graph.

Explanation:
Set C is more likely to be the one shown in the bar graph because black is more likely to be half of the brown horse.

Answer each question.
Question 36.
A bag has 5 red beads, 8 green beads, and 4 yellow beads. What is the probability of drawing a yellow bead from the bag? (Lesson 5.5)
______________
Answer:
Probability of drawing a yellow bead from the bag = 4 ÷ 17 or \(\frac{4}{17}\).

Explanation:
A bag has 5 red beads, 8 green beads, and 4 yellow beads.
Number of yellow beads = 4.
Total number of beads = Number of red beads + number of green beads + Number of yellow beads
= 5 + 8 + 4
= 13 + 4
= 17.
Probability of drawing a yellow bead from the bag = Number of yellow beads ÷ Total number of beads
= 4 ÷ 17 or \(\frac{4}{17}\).

Question 37.
Find the sum of \(\frac{1}{6}\), \(\frac{1}{6}\), and \(\frac{2}{3}\). (Lesson 6.1)
Answer:
Sum of \(\frac{1}{6}\), \(\frac{1}{6}\), and \(\frac{2}{3}\) = 1.

Explanation:
Sum = \(\frac{1}{6}\) +  \(\frac{1}{6}\) + \(\frac{2}{3}\)
=[1 + 1 + (2 × 2) ] ÷ 6
= (2 + 4) ÷ 6
= 6 ÷ 6 or \(\frac{6}{6}\)
= 1.

Question 38.
What is 1\(\frac{1}{4}\) – \(\frac{5}{8}\)? (Lesson 6.6)
Answer:
1\(\frac{1}{4}\) – \(\frac{5}{8}\) = 5 ÷ 8 or \(\frac{5}{8}\).

Explanation:
Difference:
1\(\frac{1}{4}\) – \(\frac{5}{8}\)
= (4 + 1) ÷ 4 – \(\frac{5}{8}\)
= \(\frac{5}{4}\) – \(\frac{5}{8}\)
= \(\frac{10}{8}\) – \(\frac{5}{8}\)
= (10 – 5) ÷ 8
= 5 ÷ 8 or \(\frac{5}{8}\).

Question 39.
A container and 6 lemons have a total weight of \(\frac{4}{5}\) pound. Two lemons have a total weight of pound. Find the weight of the container if all the lemons have the same weight. (Lesson 6.8)
Answer:

Explanation:

Extended Response
Solve. Show your work.
Question 40.
A clinic needs 1,350 chairs for a charity event. Three stores donate chairs. Store A donates 216 chairs, Store B donates 420 chairs, and Store C donates 376 chairs. Does the clinic have enough chairs? Decide if you need to find an estimate or an exact answer. (Lesson 2.1)
Answer:
338 more chairs are needed.

Explanation:
Number of chairs Store A donates = 216.
Number of chairs Store B donates = 420.
Number of chairs Store C donates = 376.
Total number of chairs a clinic needs for a charity event = 1,350.
Number of chairs all Stores donated = Number of chairs Store A donates + Number of chairs Store B donates + Number of chairs Store C donates
= 216 + 420 + 376
= 636 + 376
= 1012.
Difference:
Total number of chairs a clinic needs for a charity event – Number of chairs all Stores donated
= 1,350 – 1,012
= 338.

Question 41.
Barrie had some stamps. He gave \(\frac{1}{8}\) of them to Tom. If he gave 15 stamps to Tom, how many stamps did he have at first? (Lesson 6.8)
Answer:
Number of stamps he have first = 120.

Explanation:
Fraction of stamps he gave to Tom = \(\frac{1}{8}\)
Number of stamps if he gave to him = 15.
Number of stamps he have first = Number of stamps if he gave to him ÷ Fraction of stamps he gave to Tom
= 15 ÷ \(\frac{1}{8}\)
= 15 × 8
= 120.

Question 42.
Mr. Marchez ordered 7 books through a website. The total mass of the books was 3,458 grams. The masses of each book were 360 g 410 g 280 g 150 g 550 g ? ?
The masses of the remaining 2 books were not given. (Lesson 5.6)

a. Find the mean mass of the books.
Answer:
Mean mass of the books = 494 grams.

Explanation:
The mean is the average of the numbers
The masses of each book were 360 g 410 g 280 g 150 g 550 g
Total mass of all books = 3,458 grams.
Number of books = 7.
Mean mass of the books = Total mass of all books ÷ Number of books
= 3,458 ÷ 7
= 494 grams.

b. Find the mean mass of the 2 remaining books.
Answer:
Mass of the remaining 2 books = 1,708.

Explanation:
Mass of the remaining 2 books =
(Total mass of all books – Mass of 5 books)
= 3,458  – (360 + 410 + 280 + 150 + 550)
= 3,458  – (770 + 280 + 150 + 550)
= 3,458  – (1,050 + 150 + 550)
= 3,458  – (1,200 + 550)
= 3,458  – 1,750
= 1,708.

c. The range of the masses is 710 grams, and the lightest mass is given above. What is the mass of the heaviest book?
Answer:
Mass of the heaviest book = 550 grams.

Explanation:
Range of the masses = 710 grams.
The masses of each book were 360 g 410 g 280 g 150 g 550 g.
=> lightest mass = 150grams.
Mass of the heaviest book = 550 grams.

Question 43.
A factory packages 4,250 boxes of cereal. The number of oat cereal boxes is 715 more than the number of wheat cereal boxes. The number of fruit cereal boxes is 5 times the number of wheat cereal boxes. How many fruit cereal boxes does the factory package? (Lesson 3.5)
Answer:
Number of fruits cereal boxes = 2,525.

Explanation:
Number of boxes of cereal a factory packages = 4,250.
The number of oat cereal boxes is 715 more than the number of wheat cereal boxes.
Let the wheat cereal boxes be X.
=> Number of oat cereal boxes = 715 + X.
The number of fruit cereal boxes is 5 times the number of wheat cereal boxes.
=> Number of fruits cereal boxes = 5 × X = 5X.
Number of boxes of cereal a factory packages = Number of oat cereal boxes + Number of fruits cereal boxes + Number of wheat cereal boxes
=> 4250 =  (715 + X) + 5X + X
=> 4250 = 715 + X + 5X + X
=> 4250 = 715 + 2X + 5X
=> 4250 = 715 + 7X
=> 4250 – 715 = 7X
=> 3535 = 7X
=> 3535 ÷ 7 = X
=> 505 = X.
=> Number of wheat cereal boxes  = 505.
Number of oats cereal boxes = 715 + X = 715 + 505 = 1,220.
Number of fruits cereal boxes = 5X = 5 × 505 = 2,525.

Question 44.
Three people guess the number of cherries in a bag, rounded to the nearest 10. Alex guesses 80 cherries, Jess guesses 60 cherries, and Nia guesses 70 cherries. The actual number is a multiple of 7. The difference of the digits of the number is 9. Who guessed correctly? (Lesson 2.1 and 2.2)
Answer:
Nia guesses correctly.

Explanation:
Number of cherries Alex guesses = 80.
Number of cherries Jess guesses = 60.
Number of cherries Nia guesses = 70.
The actual number is a multiple of 7.
=> Factors of 70 = 1 × 70.
= 2 × 35
= 5 × 14
= 7 × 10
The difference of the digits of the number is 9.
=> 14 – 5 = 9.