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Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 6 Practice 2 Multiplying 2: Using Dot Paper to finish your assignments.

Math in Focus Grade 2 Chapter 6 Practice 2 Answer Key Multiplying 2: Using Dot Paper

Use dot paper to solve.

Question 1.
There are 4 bags. 2 rolls are in each bag. How many rolls are there in all?

4 × 2 = ____
There are ___ rolls in all.
Answer:
Explanation:
Given:
Total number of bags = four
each bag has = two rolls
Multiply four with two we get
4 × 2 = 8
There are 8 rolls in all.

Question 2.
6 bicycles are in the shop. Each bicycle has 2 wheels. How many wheels are there in all?

Answer:

Explanation:
Given:
Total number of bicycle in a shop  = six
each each bicycle has = two wheels
Multiply six with two we get
6 × 2 = 12
There are 12 wheels in all.

Use dot paper to solve.

Question 3.
Mrs. Smith buys 5 burgers for her children. Each burger costs $2. How much do the 5 burgers cost in all?

Answer:

Explanation:
Given:
Total number of burgers  Mrs. Smith buys for her children = five
Each burger costs = two dollar
Multiply four with two we get
5 × 2 =10
The five burgers cost $ 10 in all

Question 4.
Ed buys 9 pairs of socks. Each pair of socks costs $2. How much do the socks cost in all?

Answer:

Explanation:
Given:
Total number of pair of socks Ed buys = nine
Each pair of socks costs = two dollar
Multiply nine with two we get
9 × 2 = 18
The five burgers cost $ 18 in all

Use dot paper to find the missing numbers.

Example

Question 5.

Answer:

Question 6.
6 × 2 = 10 + ___
= ______
Answer:
6 × 2 = 10 + 2
= 12

Question 7.
8 × 2 = 20 – ___
= ____
Answer:
8 × 2 = 20 – 4
= 16

Use dot paper to find the missing numbers.

Example

Question 8.

Answer:

Question 9.

Answer:

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 6 Practice 4 Multiplying 5: Using Dot Paper to finish your assignments.

Math in Focus Grade 2 Chapter 6 Practice 4 Answer Key Multiplying 5: Using Dot Paper

Use dot paper to solve.

Example
Kelly uses 5 beads to make one necklace. How many beads does she use to make 8 necklaces?

8 × 5 = 40
She uses 40 beads to make 8 necklaces.

Question 1.
9 friends buy tickets to a movie. Each ticket costs $5. How much do the friends pay in all for the tickets?
_____ × $ ____ = $ ____
The pay $_____ in all for the tickets.
Answer:
9 × $5 = $45
The pay $45 in all for the tickets.
Explanation:
Given:
Number of friends are there to by tickets = 9 friends
each tickets cost  = $5
To know how much the friends have to pay in all for the tickets, we need to multiply 5 with 9 then we get
5 × 9 = 45
So, they have to pay $45 in total for the tickets

Question 2.
Ellen packs some books into 10 boxes. She packs 5 books into each box. How many books does she pack in all?
_____ × _____ = _____
She packs ____ books into 10 boxes.
Answer:
10 × 5 = 50
She packs 50 books into 10 boxes.
Explanation:
Given:
Total number of boxes Ellen packs the books into = 10
In each box she packs = 5 books
To know how many hooks in total she packs we need to multiply 10 with 5 so we get
10 × 5 = 50
In total she packs 50 books in 10 boxes.

Multiply.

Color the dots to help you.

Example

Question 3.

Answer:

Multiply.

Color the dots to help you.

Question 4.

Answer:

Use dot paper to fill in the blanks.

Question 5.

Answer:

Use dot paper to fill in the blanks.

Question 6.

Answer:

Question 7.

Answer:

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.