All the solutions provided inÂ McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Review will give you a clear idea of the concepts.

Vocabulary Check

Use the word bank below to complete each clue.

Associative
Distributive
equation
evaluate
expression
operations
variable

ACROSS
1. A number sentence that uses the equals sign.
3. The property which allows you to decompose a factor into smaller numbers.
5. A symbol or letter that stands for the unknown.
6. Addition, subtraction, multiplication, and division.

DOWN
1. A number or a combination of numbers and operations.
2. The property which states that the grouping of factors does not change the product.
4. To find the value of an expression.

Explanation:
Across are
1. A number sentence that uses the equals sign is equation.
3. The property which allows you to decompose a factor into smaller numbers is distributive property.
5. A symbol or letter that stands for the unknown is variable.
6. Addition, subtraction, multiplication, and division is operations.
Down are
1. A number or a combination of numbers and operations is expression
2. The property which states that the grouping of factors does not change the product is associative property
4. To find the value of an expression is evaluate.

Concept Check

Use the Distributive Property to find each product.

Question 7.
9 Ă— 7 = _____________

Explanation:
Given, 9 Ă— 7
By using Distributive Property we get.
9 Ă— 7 = ( 9 Ă— 5 ) + ( 9 Ă— 2 )
= 45 + 18
= 63
So, 9 Ă— 7 = 63.

Question 8.
7 Ă— 6 = _____________

Explanation:
Given, 7 Ă— 6
By using Distributive Property we get.
7 Ă— 6 = ( 7 Ă— 3 ) + ( 7 Ă— 3 )
= 21 + 21
= 42
So, 7 Ă— 6 = 42.

Use parentheses to group two factors. Then find each product.

Question 9.
1 Ă— 3 Ă— 4 = _______________

Explanation:
Given, 1 Ă— (3 Ă— 4)
Multiply the factors inside the parentheses first.
1 Ă— 12Â  = 12
So, 1 Ă— (3 Ă— 4) = 12 .

Question 10.
2 Ă— 5 Ă— 3 = _______________

Explanation:
Given, 2 Ă— (5 Ă— 3)
Multiply the factors inside the parentheses first.
2 Ă— 15Â  = 30
So, 2 Ă— (5 Ă— 3) = 30.

Use numbers and operations to write each phrase as an expression.

Question 11.
5 people equally divide $45 Answer: 45 Ă· 5 Explanation: Given,Â 5 people equally divide$45
Here divide refers to division
Then, it will be 45 Ă· 5
So, The sentence is represented by 45 Ă· 5

Question 12.
6 tables with 4 legs each
Answer: 6 Ă— 4

Explanation:
Given, 6 tables with 4 legs each
Here each refers to multiplication,
Then it will be, 6 Ă— 4
So, The sentence is represented by 6 Ă— 4

Algebra Evaluate each expression if a = 4 and b = 5.

Question 13.
3 + a
3 + ______________ = ______________

Explanation:
Given, 3 + a and a = 4
3 + 4 = 7
So, 3 + a = 7.

Question 14.
20 Ă· b + 5
_____________ + _______________ = _______________

Explanation:
Given, 20 Ă· b + 5 and b = 5
(20 Ă· 5) + 5 = 4 + 5 = 9
So, 20 Ă· b + 5 = 9.

Algebra Write an equation to represent each sentence.

Question 15.
If there are 7 cars on a roller coaster with 3 seats each and 2 seats are empty, then m seats are full.
Answer: The equation is ( 7 Ă— 3 ) – 2 = m

Explanation:
Given, If there are 7 cars on a roller coaster with 3 seats each and 2 seats are empty,
then m seats are full.
Then it will be , there are 7 cars on a roller coaster with 3 seats each is 7 Ă— 3
2 seats are empty, 2 less
that is ( 7 Ă— 3 ) – 2 = m
So, The equation is ( 7 Ă— 3 ) – 2 = m

Question 16.
There are 2 vases with 3 flowers each and each flower has m petals, so there are a total of 30 petals.
Answer: the equation is 2 Ă— ( 3 Ă— m ) = 30.

Explanation:
Given, There are 2 vases with 3 flowers each and each flower has m petals,
so there are a total of 30 petals.
That will be, 2 Ă— ( 3 Ă— m ) = 30
So, the equation is 2 Ă— ( 3 Ă— m ) = 30.

Question 17.
Bree counted 51 birds at the park. Twenty-seven were geese and the rest were ducks. The ducks flew away in groups of 8. How many groups of ducks were there? Write an equation with a letter for the unknown. Then solve.
Answer: there are 3 groups of ducks which flew away bye 8 in each group

Explanation:
Given, Bree counted 51 birds at the park. Twenty-seven were geese and the rest were ducks.
The ducks flew away in groups of 8.
let the unknown be y
51 = 27 + (y Ă·Â  8)
y = 51 – 27
y = 24
Then, 24 Ă· 8 = 3
The equation will be, 51 = 27 + (y Ă·Â  8)
So, there are 3 groups of ducks which flew away bye 8 in each group.

Problem Solving

Algebra Write an equation with a letter for the unknown for Exercises 18-19. Then solve.

Question 18.
The building manager put new door knobs on 4 doors in each apartment. There are 3 apartments on each floor and 3 floors in the apartment building. How many new door knobs did he install?
Answer: 36 new door knobs were installed by him.

Explanation:
Given, The building manager put new door knobs on 4 doors in each apartment.
There are 3 apartments on each floor and 3 floors in the apartment building.
let the unknown be y
4 Ă— 3 Ă— 3 = y
y = 4 Ă— (3 Ă— 3)
y = 4 Ă— 9
y = 36.
So, 36 new door knobs were installed by him.

Question 19.
A soccer team scored 1 point. They scored four more points. The other team had twice as many points. How many points did the other team have?
Answer: The other team have 10 points.

Explanation:
Given, A soccer team scored 1 point. They scored four more points.
The other team had twice as many points.
let the unknown be y
Then, (1+ 4 ) Ă— 2 = y
y = 5 Ă— 2
y = 10
So, The other team have 10 points.

Question 20.
Morgan needed to write an equation. Explain whether she actually wrote an equation.

Answer: No, She did not write an equation.

Explanation:
Given, Morgan needed to write an equation.
She only wrote, 3 Ă— 5
That is an expression which has numbers and basic operations
She has to write an equation with an equal sign
For example, 3 Ă— 5 = 15
So, She did not write an equation.

Test Practice

Question 21.
Kayla is x years old. Kevin is 3 years younger than Kayla. If x = 12, how old is Kevin?
(A) 7 years old
(B) 8 years old
(C) 9 years old
(D) 10 years old

Explanation:
Given, Kayla is x years old. Kevin is 3 years younger than Kayla.
That is Kevin = x – 3
If x = 12,
12 – 3 = 9
So, Kevin will be 9 years old
Option c is correct.

Reflect

Use what you learned about properties and equations to complete the graphic organizer.

Now reflect on the ESSENTIAL QUESTION ? Write your answer below.