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)