All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Lesson 7 Write Equations will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Lesson 7 Write Equations
An equation, or number sentence, shows that two expressions are equal. An equation contains an equals sign (=).
Math in My World
Example 1
Use the information shown to find the total number of red and green apples.
Write an equation to represent the counters.
Equation: ______________ + _____________ = ____________
The equation _____________ + 4 = _____________ tells us there are _____________ red and green apples.
In order to write an equation, you need to decide what operation to use. There are words and phrases that can suggest whether to add, subtract, multiply, or divide. Here are some examples.
Answer: The equation is 5 + 4 = 9
Explanation:
Given, red apples are 5,
Yellow apples are 3,
Green apples are 4,
The equation is 5 + 4 = 9
So, there are 9 red and green apples altogether,
Example 2
Hayden used his tape measure to find the total length of a board needed to finish his tree fort. When he cuts the board, one piece will be 48 inches and the other will be 32 inches. What is the total length of the board?
Write an equation to represent the problem.
Use the letter b for the unknown.
The word total suggests adding.
Example 3
A hardware store ordered 2 sets of monkey wrenches. There are 3 wrenches in each set. After the wrenches are shipped, the store will have a total of 7 wrenches. How many wrenches did they already have?
Write an equation to represent the problem. Use the letter w for the unknown.
The phrases sets and in each set suggest multiplying. The word total suggests adding.
Talk Math
What is the difference between an expression and an equation?
Answer: An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign.
Explanation:
For example, expression is 5 + y
equation is x + 8 = 0.
Guided Practice
Write an equation to represent each sentence.
Question 1.
The total of 3 letters plus 2 letters is x letters.
___________ + ____________ = ______________
Answer: 3 + 2 = x
Explanation:
Given, The total of 3 letters plus 2 letters is x letters.
The equation will be, 3 + 2 = x
x = 5
So, The sentence represents 3 + 2 = x
Question 2.
A group of 6 has x taken away and 2 are left.
___________ – ____________ = ______________
Answer: The sentence represents 6 – x = 2.
Explanation:
Given, A group of 6 has x taken away and 2 are left.
The equation will be, 6 – x = 2
x = 4
So, The sentence represents 6 – x = 2.
Independent Practice
Underline the part of the phrase that suggests which operation to use. Circle the operation.
Question 3.
the difference between a pack of flashcards and a pack of pens
addition
subtraction
multiplication
division
Answer: subtraction
Explanation:
Given, the difference between a pack of flashcards and a pack of pens
Here , difference refers to minus
So, we have to use subtraction
Question 4.
the total cost of glue, markers, and pencils
addition
subtraction
multiplication
division
Answer: addition
Explanation:
Given, the total cost of glue, markers, and pencils
Here the total refers to plus
So, we have to use addition
Question 5.
the number of crayons equally separated into each box
addition
subtraction
multiplication
division
Answer: division
Explanation:
Given, the number of crayons equally separated into each box
Here, separation refers to divide
So, we have to use division.
Algebra Write an equation to represent each sentence.
Question 6.
9 inches less than 14 inches is y inches.
Answer: The sentence will be represented as 9 – 14 = y.
Explanation:
Given, 9 inches less than 14 inches is y inches.
Here, less than refers to subtraction,
The equation will be , 9 – 14 = y
So, The sentence will be represented as 9 – 14 = y.
Question 7.
24 hammers are divided into y equal sets of 3.
Answer: The sentence will be represented as 24 ÷ y = 3.
Explanation:
Given, 24 hammers are divided into y equal sets of 3.
Here, divided refers to division
The equation will be , 24 ÷ y = 3
So, The sentence will be represented as 24 ÷ y = 3.
Question 8.
12 fish minus y fish plus 4 more equals 9 fish.
Answer: The sentence will be represented as 12 – y + 4 = 9
Explanation:
Given, 12 fish minus y fish plus 4 more equals 9 fish.
Here, minus refers to subtraction, plus and more refers to addition
The equation will be , 12 – y + 4 = 9
So, The sentence will be represented as 12 – y + 4 = 9
Question 9.
5 games plus two times as many is y games.
Answer: The sentence will be represented as 5 + 2 × 5 = y
Explanation:
Given, 5 games plus two times as many is y games.
Here, plus refers to addition and times as many refers to multiplication,
The equation will be , 5 + 2 × 5 = y
So, The sentence will be represented as 5 + 2 × 5 = y
Algebra Use the numbers in the table for Exercises 10-12 to write an equation for each sentence.
Question 10.
The difference between the number of nails and hooks is m hooks.
Answer: 14 – 6 = m
Explanation:
Given, The difference between the number of nails and hooks is m hooks.
Here, difference refers to subtraction
from the picture above we know that , nails = 14 and hooks = 6
the equation will be 14 – 6 = m
So, m = 8.
Question 11.
The number of hooks, springs, and bolts altogether is t tools.
Answer: The sentence will be represented by 6 + 2 + 7 = t.
Explanation:
Given, The number of hooks, springs, and bolts altogether is t tools.
Here altogether refers to addition
Then, 6 + 2 + 7 = t
So, The sentence will be represented by 6 + 2 + 7 = t.
Question 12.
Half the number of hooks plus the number of nails is n tools.
Answer: The sentence will be represented by 6 ÷ 2 + 14 = n
Explanation:
Given, Half the number of hooks plus the number of nails is n tools.
Here, Half refers to division , plus refers to addition.
Then, 6 ÷ 2 + 14 = n
So, The sentence will be represented by 6 ÷ 2 + 14 = n
Problem Solving
Mathematical PRACTICE Use Algebra Write an equation using any letter for the unknown.
Question 13.
Steph used some nails from the toolbox. Her dad used 9 nails. How many nails did Steph use if they used 17 nails altogether?
Answer: Steph used 8 nails.
Explanation:
Given, Steph used some nails from the toolbox. Her dad used 9 nails.
Let the unknown be y and
if they used 17 nails altogether
then it will be y + 9 = 17
y = 17 – 9 = 8
So, Steph used 8 nails.
Question 14.
Twenty customers ordered sandwiches. Three ordered a ham sandwich. Thirteen ordered a chicken sandwich. The rest ordered a turkey sandwich. How many customers ordered a turkey sandwich?
Answer: 4 members ordered a turkey sandwich.
Explanation:
Given, Twenty customers ordered sandwiches. Three ordered a ham sandwich.
Thirteen ordered a chicken sandwich. The rest ordered a turkey sandwich.
let the unknown be y
Then, 3 + 13 + y = 20
y = 20 – 16
y = 4
so, 4 members ordered a turkey sandwich.
Question 15.
Al gave his iguana 12 beans. The iguana ate half of them by noon. How many beans were left at the end of the day if the iguana ate 4 more?
Answer: there are 2 beans left.
Explanation:
Given, Al gave his iguana 12 beans. The iguana ate half of them by noon.
if the iguana ate 4 more
Then, 12 ÷ 2 + 4 ,
The expression will be, 12 ÷ 2 + 4
= 6 + 4
That is 10 beans finished by iguana
So, there are 2 beans left
HOT Problems
Question 16.
Mathematical PRACTICE Model Math Write a real-world problem that can be solved using the equation 16 ÷ 2 – 3 = n.
Answer: Detailed explanation is given below,
Explanation:
Given, 16 ÷ 2 – 3 = n.
There are 24 carrots in which 16 are divided equally among 2 friends and then gave another 3 to another friend , then how many carrots are left with the person.
There will 5 carrots left out.
Question 17.
Building on the Essential Question How are letters and symbols used in equations?
Answer: symbols (usually letters) are used to represent numbers.
To solve math problems, you should know what variables and constants are.
Explanation:
For example,
y = 5 + z
Here, + is the symbol for addition and
y and z are the letters which are considered as variables and constants.
McGraw Hill My Math Grade 3 Chapter 9 Lesson 7 My Homework Answer Key
Practice
Algebra Write an equation to represent each sentence.
Question 1.
Five more than 7 shells is s.
Answer: 5 + 7 = s
Explanation:
Given, Five more than 7 shells is s.
Here, plus refers to addition,
The equation will be , 5 + 7 = s
So, The sentence will be represented as 5 + 7 = s.
Question 2.
Four times as many as 4 pencils is p.
Answer: 4 × 4 = p
Explanation:
Given, Four times as many as 4 pencils is p.
Here, times as many refers to multiplication,
The equation will be , 4 × 4 = p
So, The sentence will be represented as 4 × 4 = p.
Question 3.
Half as many as 18 squirrels is x.
Answer: (18 ÷ 2) × 18 = x
Explanation:
Given, Half as many as 18 squirrels is x.
Here, as many as refers to multiplication,
The equation will be , (18 ÷ 2) × 18 = x
So, The sentence will be represented as (18 ÷ 2) × 18 = x
Question 4.
Eleven spoons minus s equals 9 spoons.
Answer: 11 – s = 9.
Explanation:
Given, Eleven spoons minus s equals 9 spoons.
Here, minus refers to subtraction,
The equation will be , 11 – s = 9
So, The sentence will be represented as 11 – s = 9.
Question 5.
3 more than 14 eggs divided into 2 equal groups is e.
Answer: ( 3 + 14 ) ÷ 2 = e
Explanation:
Given, 9 inches less than 14 inches is y inches.
Here, more than refers to addition,
The equation will be , ( 3 + 14 ) ÷ 2 = e
So, The sentence will be represented as ( 3 + 14 ) ÷ 2 = e.
Question 6.
5 boxes of muffins with m number in each box equals 30.
Answer: 5 × m = 30
Explanation:
Given, 5 boxes of muffins with m number in each box equals 30.
Here, in each refers to multiplication,
The equation will be , 5 × m = 30
So, The sentence will be represented as 5 × m = 30.
Question 7.
The total of 13 cherries, 8 more cherries, and 2 more cherries is c.
Answer: 13 + 8 + 2 = c
Explanation:
Given, The total of 13 cherries, 8 more cherries, and 2 more cherries is c.
Here, more refers to addition,
The equation will be , 13 + 8 + 2 = c
So, The sentence will be represented as 13 + 8 + 2 = c.
Question 8.
32 tennis balls shared equally by 4 players plus 3 more is b.
Answer: 32 ÷ 4 + 3 = b
Explanation:
Given, 32 tennis balls shared equally by 4 players plus 3 more is b.
Here, plus refers to addition,
The equation will be , 32 ÷ 4 + 3 = b
So, The sentence will be represented as 32 ÷ 4 + 3 = b
Problem Solving
Mathematical PRACTICE Use Algebra Write an equation using any letter for the unknown.
Question 9.
Irving paid for his lunch with a $10 bill and got $6 back in change. How much did his lunch cost?
Answer: the lunch cost $4.
Explanation:
Given, Irving paid for his lunch with a $10 bill and got $6 back in change.
Here, change refers to subtraction,
Let y be the unknown ,
10 – y = 6
y = 10 – 6 = 4
The equation will be , 10 – y = 6
So, the lunch cost $4.
Question 10.
Erin’s beagle weighs 35 pounds. Her Great Dane weighs twice as much as the beagle plus 2 more pounds. How much does the Great Dane weigh?
Answer: Great Dane weighs 72 pounds.
Explanation:
Given, Erin’s beagle weighs 35 pounds.
Her Great Dane weighs twice as much as the beagle plus 2 more pounds.
Here, twice as much as refers to multiplication,
let the known be y,
The equation will be , ( 35 × 2 ) + 2 = y
70 + 2 = y
y = 72,
So, Great Dane weighs 72 pounds.
Vocabulary Check
Question 11.
Explain the difference between an expression and an equation.
Answer: An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
An equation is made up of two expressions connected by an equal sign.
Explanation:
Word example: The sum of 8 and 3 is equal to 11.
8 + 3 = 11.
Test Practice
Question 12.
Venus bought 3 loaves of bread that have 20 slices each. Then she used 2 slices to make a sandwich. There are b slices left. Which equation represents the situation?
(A) 3 × 20 – 2 = b
(B) 3 + 20 – 2 = b
(C) (3 × 20) ÷ 2 = b
(D) 3 + 20 – b = 2
Answer: A
Explanation:
Given, Venus bought 3 loaves of bread that have 20 slices each.
Then she used 2 slices to make a sandwich.
There are b slices left.
The equation will be, 3 × 20 – 2 = b
So, option A represents the given sentence.