All the solutions provided in **McGraw Hill My Math Grade 5 Answer Key PDF Chapter 7 Lesson 3 Write Numerical Expressions** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 7 Lesson 3 Write Numerical Expressions

**Math in My World**

**Example 1**

Terrell went to dinner with his friends and ordered 3 tacos. Each taco costs $2 and he has a coupon for a dollar off his purchase. The total cost in dollars of Terrell’s purchase is represented by the phrase multiply three by two, then subtract one. Write the total cost as a numerical expression.

Question 1.

Write the phrase in parts.

Part 1 multiply three by ___________

Part 2 then subtract ___________

Answer:

\(\frac{3}{2}\) – 1 = $1

Explanation:

Terrell ordered 3 tacos.

Each taco costs $2.

He has a coupon for a dollar off his purchase.

The total cost in dollars of Terrell’s purchase is,

\(\frac{3}{2}\) – 1 = $1

Question 2.

Write each part as a numerical expression.

Part 1 multiply three by two _________

Part 2 then subtract one ___________

Answer:

\(\frac{3}{2}\) – 1

Explanation:

Part 1 multiply three by two \(\frac{3}{2}\)

Part 2 then subtract one \(\frac{3}{2}\) – 1 = $1

Question 3.

Combine the numerical expressions to represent the total cost in dollars. Add parentheses if needed.

Answer:

$1

Explanation:

Terrell ordered 3 tacos.

Each taco costs $2.

He has a coupon for a dollar off his purchase.

The total cost in dollars of Terrell’s purchase is,

multiply three by two, then subtract one.

\(\frac{3}{2}\) – 1 = $1

**Example 2**

A ticket to a baseball game costs $25 and popcorn is $8. Three friends bought tickets and popcorn. The expressions below give the cost for one friend and for three friends. Compare the two expressions without evaluating them.

One Friend

25 + 8

Three Friends

(25 + 8) × 3

Both expressions contain the same addition expression. Write the addition expression. ____________

For three friends, the addition expression is multiplied by ____________.

So, the second expression is ____________ times as large as the first expression.

Answer:

3 times as large as the first expression.

Explanation:

A ticket to a baseball game costs $25 and popcorn is $8.

25 + 8 = 33

Three friends bought tickets and popcorn.

(25 + 8) x 3

33 x 3 = 99

Compare the two expressions,

So, the second expression is 3 times as large as the first expression.

**Guided Practice**

Question 1.

Write the phrase add 7 and 11, then divide by 2 as a numerical expression.

Write the phrase in parts.

Part 1 ____________

Part 2 ____________

Write each part as a numerical expression.

Part 1 add 7and 11 __________

Part 2 then divide by 2 ___________

Combine the numerical expressions. Add parentheses if needed.

Answer:

The phrase in parts.

Part 1 add 7 and 11.

Part 2 divide by 2

Write each part as a numerical expression.

Part 1 add 7and 11 7 + 11

Part 2 then divide by 2 ÷ 2

Combine the numerical expressions.

(7 + 11) ÷ 2

Explanation:

(7 + 11) ÷ 2

18 ÷ 2 = 9

**Independent Practice**

**Write each phrase as a numerical expression.**

Question 2.

divide 15 by 3, then add 13 _____________

Answer:

(15 ÷ 3) + 13

Explanation:

Write the phrase in parts.

Part 1 15 divided by 3.

Part 2 then add 13

Write each part as a numerical expression.

Part 1 15 divided by 3 (15 ÷ 3)

Part 2 then add 13 + 13

Combine the numerical expressions.

(15 ÷ 3) + 13

Question 3.

subtract 4 from 20, then divide by 2 _____________

Answer:

(20 – 4) ÷ 2

Explanation:

Write the phrase in parts.

Part 1 subtract 4 from 20.

Part 2 then divided by 2

Write each part as a numerical expression.

Part 1 subtract 4 from 20 (20 – 4)

Part 2 then divided by 2 ÷ 2

Combine the numerical expressions.

(20 – 4)÷ 2

Question 4.

add 9 and 4, then multiply by 2 _____________

Answer:

(9 + 4) x 2

Explanation:

Write the phrase in parts.

Part 1 add 9 and 4,

Part 2 then multiply by 2

Write each part as a numerical expression.

Part 1 add 9 and 4 9 + 4

Part 2 then multiply by 2 x 2

Combine the numerical expressions.

(9 + 4) x 2

**Mathematical PRACTICE** Make Sense of Problems Compare each pair of numerical expressions without evaluating them.

Question 5.

Expression 1

(7 × 4) ÷ 2

Expression 2

7 × 4

Both expressions contain the same multiplication expression.

Write the multiplication expression _____________

In Expression 1, the product is divided by _____________.

So, Expression 1 is _____________ as small as Expression 2.

Answer:

Expression 1

(7 × 4) ÷ 2

Expression 2

7 × 4

Both expressions contain the same multiplication expression.

Write the multiplication expression 7 x 4

In Expression 1, the product is divided by 28 ÷ 2 = 14.

So, Expression 2 is 2 times as larger as Expression 1.

Explanation:

7 x 4 = 28

(7 × 4) ÷ 2 = 28 ÷ 2 = 14

Compare both the expressions,

So, Expression 2 is 2 times as larger as Expression 1.

Question 6.

Expression 1

2 + 5 + 8

Expression 2

4 × (2 + 5 + 8)

Both expressions contain the same addition expression. Write the addition expression. _____________

In Expression 2, the addition expression is multiplied by _____________.

So, Expression 2 is _____________ times as large as Expression 1.

Answer:

Expression 1

2 + 5 + 8

Expression 2

4 × (2 + 5 + 8)

Both expressions contain the same addition expression. Write the addition expression.

2 + 5 + 8

In Expression 2, the addition expression is multiplied by 4.

So, Expression 2 is 4 times as large as Expression 1.

Explanation:

2 + 5 + 8 = 15

4 × (2 + 5 + 8)

4 x 15 = 60

Compare 1 and 2 expressions, expression 2 is 4 times larger than expression 1.

60 ÷ 15 = 4 times.

**Problem Solving**

Question 7.

Robin wants to find the area of the triangle below. To find the area of a triangle, multiply the base times the height and then divide by 2. The base and height of the triangle are shown. Represent the area of the triangle with a numerical expression.

Answer:

Area of a triangle = (4 x 3) ÷ 2 square in.

Explanation:

The area of a triangle = \(\frac{base × height}{2}\)

multiply the base times the height and then divide by 2.

The base and height of the triangle are shown in the above figure

base = 4 in; height = 3 in.

So, the area of the triangle with a numerical expression.

A = (4 x 3) ÷ 2 square in.

Question 8.

Deirdre doubled her savings account balance of $100. Then she withdrew $30 to buy some new clothes. Represent this situation with a numerical expression.

Answer:

($100 x 2) – 30 OR ($100 + $100) – 30

Explanation:

Deirdre doubled her savings account balance of $100.

$100 x 2 OR $100 + $100 = $200

Then she withdrew $30 to buy some new clothes.

$200 – $30 = $170

So, the numerical expression is ($100 x 2) – 30 OR ($100 + $100) – 30

**HOT Problems**

Question 9.

**Mathematical PRACTICE** Use Number Sense Explain why the numerical expression 3 less than 16 is written as 16 – 3 and not 3 – 16.

Answer:

16 – 3 is not written as 3 – 16.

Explanation:

Because it is 16 subtract 3,

but not 3 subtract 16 because the difference would come out to a negative integer.

Question 10.

**Mathematical PRACTICE** Identify Structure Circle the numerical expression that is four times as large as 52 – 9.

52 – (9 × 4)

(52 – 9) + 4

(52 – 9) × 4

(52 – 9) ÷ 4

Answer:

Explanation:

Expression 1 is subtract 9 from 52

(52 – 9)

Expression 2 is multiply with, as it is four times as large as (52 – 9)

combine both the expressions,

(52 – 9) x 4

Question 11.

**Building on the Essential Question** How do I compare numerical expressions without calculating them?

Answer:

By comparing the difference between the given expressions.

Explanation:

For example;

Expression 1:

10 x 4 = 40

Expression 2:

10 x 8 = 80

By comparing both the expressions,

expression 2 is 4 times as large as expression 1.

### McGraw Hill My Math Grade 5 Chapter 7 Lesson 3 My Homework Answer Key

**Practice**

Question 1.

Compare the two numerical expressions without evaluating them.

Expression 1

8 – 3

Expression 2

(8 – 3) × 4

Both expressions contain the same subtraction expression.

Write the subtraction expression. _____________

In Expression 2, the difference is multiplied by _____________.

So, Expression 2 is _____________ times as large as Expression 1.

Answer:

So, Expression 2 is 4 times as large as Expression 1.

Explanation:

Expression 1

8 – 3

Expression 2

(8 – 3) × 4

Both expressions contain the same subtraction expression.

Write the subtraction expression. (8 – 3)

In Expression 2, the difference is multiplied by 5 x 4.

So, Expression 2 is 4 times as large as Expression 1.

**Problem Solving**

Question 2.

Jeffrey purchased and downloaded 12 songs on Monday. He purchased an additional 3 songs on Tuesday. The cost to download each song is $2. Write a numerical expression to represent this situation.

Answer:

2 x (12 + 3)

Explanation:

Jeffrey purchased and downloaded 12 songs on Monday.

He purchased an additional 3 songs on Tuesday.

12 + 3

The cost to download each song is $2.

Numerical expression is 2 x (12 + 3)

Question 3.

Mora bought 3 bags of apples for her class. One full bag has 8 apples, and each apple weighs 6 ounces. Write a numerical expression to represent this situation.

Answer:

3 x 8 x 6

Explanation:

Mora bought 3 bags of apples for her class.

One full bag has 8 apples,

Each apple weighs 6 ounces.

Numerical expression is 3 x 8 x 6

Question 4.

**Mathematical PRACTICE** Use Number Sense Jane wants to find the area of the trapezoid. To find the area of a trapezoid, add the two bases, multiply by the height, then divide by 2. The bases and height of the trapezoid are shown Represent the area of the trapezoid with a numerical expression.

Answer:

A = ½ (3 + 7) x 3

Explanation:

The area of a trapezoid (A ) with bases are ‘a’ and ‘b’ and height is ‘h’ is = ½ (a + b) h.

The two bases are 3m and 7m; height is 3m.

Numerical expression of area of trapezoid is,

A = ½ (3 + 7) x 3

**Vocabulary Check**

Question 5.

Fill in the blank with the correct term or number to complete the sentence.

A _____________ expression like (3 + 5) × (4 – 1) is a combination of numbers and at least one operation.

Answer:

Numerical.

Explanation:

A numerical expression in mathematics can be a combination of numbers, and integers combined using at least one mathematical operation such as addition, subtraction,

multiplication or division.

**Test Practice**

Question 6.

Denzel and three friends go to the movies. Each person buys a movie ticket for $8, a snack for $4, and a drink for $2. Which numerical expression represents the total cost of the trip to the movies for Denzel and his friends?

(A) 4 + ($8 × $4 × $2)

(B) 4 × ($8 + $4 + $2)

(C) (4 × $8) + ($4 × $2)

(D) (4 × $8 + $4) + (4 × $4 + $2)

Answer:

Option(B)

Explanation:

Each person buys a movie ticket for $8, a snack for $4, and a drink for $2.

The numerical expression represents the total cost of the trip to the movies,

Denzel and his friends together are 1 + 3 = 4 members.

4 × ($8 + $4 + $2)