All the solutions provided in McGraw Hill Math Grade 3 Answer Key PDF Chapter 5 Lesson 5 Inverse Operations will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 5 Lesson 5 Inverse Operations
Math in My World
Example 1
A baker has made a tray of fresh muffins. Use the array to write a related multiplication and division sentence to find the unknown. How many muffins are there in all?
The unknown is ___.
So, there are ___ muffins in all.
The multiplication sentence multiplies 3 by ___ to get 12. The division sentence undoes the multiplication by dividing 12 by 3 to get _____.
Answer:
The unknown is 12.
there are 12 muffins in all.
The multiplication sentence multiplies 3 by 4 to get 12. The division sentence undoes the multiplication by dividing 12 by 3 to get 4
Explanation:
A group of related facts using the same numbers is a fact family. Each fact family follows a pattern by using the same numbers.
Fact Family 3, 4 and 12
3 × 4 = 12
4 × 3 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
Fact Family 7 and 49
7 × 7 =49
49 ÷ 7 = 7
Example 2
Complete the fact family for the numbers 3, 6, and 18.
The pattern shows that 3, 6, and 18 are used in each number sentence.
Answer:
The pattern shows that 3, 6, and 18 are used in each number sentence is called a multiplication or division sentence.
Explanation:
Guided Practice
Use the arrays to find each unknown.
Question 1.
× 5 = 15
? ÷ 3 = 5
= ____
? = ____
Answer:
3, 15
Explanation:
Given,
× 5 = 15
? ÷ 3 = 5
x × 5 = 15
x = 15 ÷ 5
x = 3
? ÷ 3 = 5
? = 5 × 3
? = 15
The unknown numbers are 3 and 15.
Question 2.
4 × ? = 24
24 ÷ = 6
? = ____
= ____
Answer:
6, 4
Explanation;
Given,
4 × ? = 24
24 ÷ = 6
Let us find the answer
4 × ? = 24
? = 24 ÷ 4
? = 6
24 ÷ = 6
24 ÷ x = 6
x = 24 ÷ 6
x = 4
The unknown numbers are 6 and 4.
Question 3.
Write the fact family for 2, 6, and 12.
Answer:
The given fact family is a multiplication or division fact family.
Explanation:
Talk Math
Why are the product and the dividend the same in 3 × 7 = 21 and 21 ÷ 3 = 7?
Answer:
Division is the inverse operation of multiplication. So the product and the dividend are the same in 3 × 7 = 21 and 21 ÷ 3 = 7.
Explanation:
Given,
3 × 7 = 21 and 21 ÷ 3 = 7.
The dividend is 21, the divisor is 3.
If we multiply the given factors the product we get is 21.
3 × 7 = 21
Therefore the product and the dividend are the same.
Independent Practice
Algebra Use the arrays and inverse operations to find each unknown.
Question 4.
× 2 = 8
? ÷ 4 = 2
= ____
? = _____
Answer:
4, 8
Explanation:
Given,
× 2 = 8
x × 2 = 8
x = 8 ÷ 2
x = 4
? ÷ 4 = 2
? = 4 × 2
? = 8
The unknown numbers are 4 and 8.
Question 5.
2 × ? = 4
4 ÷ ? = 2
? = _____
Answer:
2, 2
Explanation:
Given,
2 × ? = 4
? = 4 ÷ 2
x = 2
4 ÷ ? = 2
4 ÷ 2 =?
? = 2
The unknown numbers are 2 and 2.
Question 6.
? × 2 = 14
÷ 2 = 7
= _____
? = _____
Answer:
7, 14
Explanation:
Given,
? × 2 = 14
÷ 2 = 7
Let us solve the given question
? × 2 = 14
x × 2 = 14
x = 14 ÷ 2
x = 7
÷ 2 = 7
x ÷ 2 = 7
x = 7 × 2
x = 14
The unknown numbers are 7 and 14.
Question 7.
4 × = 20
20 ÷ = 4
= _____
Answer:
5, 5
Explanation:
Given,
4 × = 20
4 × x = 20
x = 20 ÷ 4
x = 5
20 ÷ = 4
20 ÷ x = 4
20 ÷ 4 = x
x = 5
The unknown numbers are 5 and 5.
Write the fact family for each set of numbers.
Question 8.
2, 3, 6
____ _____
____ _____
Answer:
Multiplication or division sentence fact family.
Explanation:
Given,
The set of numbers is 2, 3, and 6.
The multiplication sentence
2 × 3 = 6
3 × 2 = 6
The division sentence is
6 ÷ 2 = 3
6 ÷ 3 = 2
Question 9.
2, 7, 14
____ _____
____ _____
Answer:
The fact family for each set of numbers is a Multiplication or division sentence fact family.
Explanation:
Given,
The set of numbers are 2, 7, 14
2 × 7 = 14
7 × 2 = 14
14 ÷ 2 = 7
14 ÷ 7 = 2
Question 10.
4, 8, 32
____ _____
____ _____
Answer:
The fact family for each set of numbers is a Multiplication or division sentence fact family.
Explanation:
Given,
The set of numbers is 4, 8, 32
The multiplication sentence 4 × 8 = 32
8 × 4 = 32
Division sentence 32 ÷ 4 =8
32 ÷ 8 = 4
Question 11.
4, 3, 12
____ _____
____ _____
Answer:
The fact family for each set of numbers is a Multiplication or division sentence fact family.
Explanation:
The set of numbers is 4, 3, and 12.
The multiplication sentence is 4 × 3 = 12
3 × 4 = 12
Division sentence is 12 ÷ 3 = 4
12 ÷ 4 = 3
Write the set of numbers for each fact family.
Question 12.
5 × 9 = 45
9 × 5 = 45
45 ÷ 9 = 5
45 ÷ 5 = 9
Answer:
Multiplication and Division fact family.
Explanation:
Given,
5 × 9 = 45
9 × 5 = 45
The given question is a multiplication family.
45 ÷ 9 = 5
45 ÷ 5 = 9
The given question is Division family.
Question 13.
7 × 4 = 28
4 × 7 = 28
28 ÷ 7 = 4
28 ÷ 4 = 7
Answer:
Multiplication and Division fact family.
Explanation:
Given,
7 × 4 = 28
4 × 7 = 28 is called a multiplication fact family.
28 ÷ 7 = 4
28 ÷ 4 = 7 is called a Division fact family.
Question 14.
3 × 3 = 9
9 ÷ 3 = 3
Answer:
Multiplication Sentence and Divison Sentence.
Explanation:
Given,
3 × 3 = 9
The given question is called a multiplication sentence.
9 ÷ 3 = 3 is called a Divison Sentence.
Problem Solving
Write a division sentence to solve.
Question 15.
All 5 members of the Malone family went to the movies. Their tickets cost a total of $30. How much was each ticket?
Answer:
$30 ÷ 5 = $6
Explanation:
No of members = 5
Total cost of ticket = $30
To find: How much was each ticket?
The division sentence is $30 ÷ 5 = $6
Therefore each ticket cost is $6.
Question 16.
The petting zoo has 21 animals. There are an equal number of goats, ponies, and cows. How many of each animal are there?
Answer:
21 ÷ 3 = 7.
Explanation:
No of animals = 21
There are an equal number of goats, ponies, and cows
Total of 3 equal numbers of animals.
The division sentence is 21 ÷ 3 = 7.
Question 17.
Mathematical PRACTICE 5 Use Math Tools Mr. Thomas travels 20 miles each week to and from work. If he works 5 days a week, how many miles does Mr. Thomas travel each day to go to work?
Answer:
20 ÷ 5 = 4 miles.
Explanation:
Mr. Thomas traveled each week = 20 miles.
He worked for days a week.
The division sentence is 20 ÷ 5 = 4 miles.
Therefore Mr. Thomas traveled each day to go to work is 4 miles.
HOT Problems
Question 18.
Mathematical PRACTICE 3 Draw a Conclusion Look back to Exercise 14 on the previous page. Why are there only 2 numbers in each fact family instead of 3 numbers?
Answer:
The factors given are 3 and 3 and the product is 9.
The division is an inverse operation of multiplication
If we write 3 × 3 =9
The inverse multiplication is 3 × 3 =9
As per division
9 ÷ 3 = 3
Question 19.
? Building on the Essential Question How can I use multiplication facts to remember division facts? Give an example.
Answer:
When multiplying or dividing we can use the fact from the inverse operations. Let us know more with a simple example.
Explanation:
Example:
If we know 4 × 6 = 24
and we also know the related division fact 24 ÷ 4 = 6 or 24 ÷ 6 = 4.
McGraw Hill My Math Grade 3 Chapter 5 Lesson 5 My Homework Answer Key
Practice
Algebra Use the array to find each unknown.
Question 1.
× 4 = 20
? ÷ 5 = 4
= ____
? = ____
Answer:
5, 20
Explanation:
Given,
x × 4 = 20
x = 20 ÷ 4
x = 5
? ÷ 5 = 4
20 ÷ 5 = 4
Therefore the unknowns are 5 and 4.
Question 2.
4 × = 16
? ÷ 4 = 4
= ____
? = ____
Answer:
4, 16
Explanation:
The number of rows is 4 no of the columns is 4
4 × 4 = 16
? ÷ 4 = 4
x ÷ 4 = 4
16 ÷ 4 = 4
The unknown numbers are 4 and 16.
Question 3.
7 × = 21
? ÷ 7 = 3
= ____
? = ____
Answer:
3, 21
Explanation:
Given,
7 × = 21
? ÷ 7 = 3
Now let’s find out the given question
7 × x = 21
x = 21 ÷ 7
x = 3
? ÷ 7 = 3
21 ÷ 7 = 3
Question 4.
2 × = 12
? ÷ 2 = 6
= ____
? = ____
Answer:
6, 12
Explanation:
Given,
2 × = 12
? ÷ 2 = 6
Now let us solve this
2 × = 12
2 × x = 12
x = 12 ÷ 2
x = 6
? ÷ 2 = 6
12 ÷ 2 = 6
Write the fact family for each set of numbers.
Question 5.
5, 8, 40
Answer:
Multiplication or Division fact family.
Explanation:
The set of numbers given is 5, 8, and 40.
5 × 8 = 40
8 × 5 = 40
40 ÷ 8 = 5
40 ÷ 5 = 8
Question 6.
6, 7, 42
Answer:
Multiplication or Division fact family.
Explanation:
The set of numbers given is 5, 8, and 40.
6 × 7 = 42
7 × 6 = 42
42 ÷ 6 = 7
42 ÷ 7 = 6
Write the set of numbers for each fact family.
Question 7.
4 × 9 = 36 36 ÷ 4 = 9
9 × 4 = 36 36 ÷ 9 = 4
Answer:
4, 9, 36
Explanation:
The set of numbers is 4, 9, and 36.
The given fact family is a Multiplication or Division, fact family.
Question 8.
2 × 8 = 16 16 ÷ 2 = 8
8 × 2 = 16 16 ÷ 8 = 2
Answer:
2, 8, 16
Explanation:
The set of numbers is 2, 8, and 16.
The given fact family is a Multiplication or Division fact family.
Problem Solving
Question 9.
Mathematical PRACTICE Model Math Tia has $35 to spend on socks for the family. If each pair of socks costs $5, how many pairs can she buy? Write a division sentence to solve.
Answer:
$35 ÷ $5 = 7 pairs
Explanation:
Given,
Tia spent on socks = $35
Cost of each pair = $5
The division sentence is $35 ÷ $5 = 7 pairs.
Hence she bought 7 pairs.
Vocabulary Check
Draw a line to connect each vocabulary word with its definition.
Answer:
Test Practice
Question 15.
Which pair shows inverse operations?
A. 2 × 2 = 4; 4 ÷ 2 = 2
B. 2 × 2 = 4; 4 – 2 = 2
C. 2 × 2 = 4; 8 ÷ 4 = 2
D. 2 × 2 = 4; 4 ÷ 4 = 1
Answer:
A. 2 × 2 = 4; 4 ÷ 2 = 2
Explanation:
The pair that shows the inverse operation is A. 2 × 2 = 4; 4 ÷ 2 = 2
Division sentence is 4 ÷ 2 = 2
Multiplication sentence = 2 × 2 = 4