All the solutions provided in **McGraw Hill Math Grade 4 Answer Key PDF Chapter 2 Lesson 1 Addition Properties and Subtraction Rules** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 2 Lesson 1 Addition Properties and Subtraction Rules

**Math in My World**

Example 1

Carlos is buying the items shown. Does the order in which the musical instruments are scanned change the total cost?

The order in which the instruments are scanned does not change the total cost. This is the Commutative Property of Addition.

So, the total cost will be $30

Example 2

There were 16 people at the pool on Saturday. There were no people at the pool on Sunday. How many people were there on Saturday and Sunday?

16 + 0 = 16 This is the Identity Property of Addition.

So, there were 16 people at the pool on Saturday and Sunday.

You can use properties and rules to find the unknown, or missing number, in a number sentence.

Example 3

Find the unknown in 10 – = 10.

When you subtract 0 from any number, the result is the number, So, the unknown is 0

**Talk Math**

Which subtraction rule is like the opposite of the Identity Property of Addition? Explain your reasoning.

**Guided Practice**

**Find each unknown. Draw a line to identify the property or rule used.**

Answer:

**Independent Practice**

**Algebra Find each unknown. Write each property or rule that is used.**

Question 4.

( + 8) + 7 = 9 + (8 + 7)

= ___

Answer: Associative property is used and the unknown is 9

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

( 9 + 8 ) + 7 = 9 + ( 8 + 7 )

24 = 24

Here the result remained same ,

So, The property used here is Associative property

Question 5.

14 + 13 = 13 +

= ____

Answer: commutative property is used and the unknown is 14

Explanation:

The property which states that the order in which two numbers are added does not change the sum is Commutative property

14 + 13 = 13 + 14

27 = 27

So, The property used is commutative property

Question 6.

+ 0 = 19

= ____

Answer: Identity property is used and the unknown is 19

Explanation:

For any number, zero plus that number is the number is called Identity property of addition

19 + 0 = 19

When you add any number to 0 the resultant will be the number .

So, the property used is Identity property

Question 7.

25 – = 0

= ____

Answer: subtraction of the same number and unknown is 25

Explanation:

25 – 25 = 0

So, the same number is subtracted form the number , the resultant will be 0

Question 8.

17 + (11 + 18) = (17 + ) + 18

= ____

Answer: Associative property is used and the unknown is 11

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

17 + ( 11 + 18 ) = ( 17 + 11 ) + 18

46 = 46

So, The property used is Associative property of addition.

Question 9.

37 – = 37

= ____

Answer: Identity property of subtraction and the unknown is 0.

Explanation:

For any number, zero plus that number is the number is called Identity property of addition

37 – 0 = 37

So, the result remained unchanged , the property used is Identity property of subtraction.

**Use the properties of addition to add.**

Problem Solving

Question 10.

17 + 0 = ___

Answer: 17

Explanation:

For any number, zero plus that number is the number is called Identity property of addition

17 + 0 = 17

Identity property of addition is used.

Question 11.

(22 + 35) + 15 = ____

Answer: 72

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

(22 + 35) + 15 = 72

Associative property is used.

Question 12.

16 + 22 = ____

Answer: 38

Explanation:

The property which states that the order in which two numbers are added does not change the sum is Commutative property

16 + 22 = 38

Commutative property is used

Question 13.

0 + 47 = ____

Answer: 47

Explanation:

For any number, zero plus that number is the number is called Identity property of addition

0 + 47 = 47

Identity property is used.

Question 14.

19 + (61 + 15) = ___

Answer: 95

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

19 + (61 + 15) = 95

Associative property is used.

Question 15.

27 + (43 + 16) = ____

Answer: 86

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

27 + (43 + 16) = 86

Associative property is used.

Question 16.

23 + 74 = ____

Answer: 97

Explanation:

The property which states that the order in which two numbers are added does not change the sum is Commutative property

23 + 74 = 97

Commutative property is used

Question 17.

(24 + 24) + 16 = ____

Answer: 64

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

(24 + 24) + 16 = 64

Associative property is used.

Question 18.

0 + 83 = ___

Answer: 83

Explanation:

For any number, zero plus that number is the number is called Identity property of addition

0 + 83 = 83

identity property is used

Question 19.

25 + (35 + 19) = ____

Answer: 79

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

25 + (35 + 19) = 79

Associative property is used

**Problem Solving**

Question 20.

Paco has 75 minutes before he needs to get ready for baseball practice. He cleans his room for 40 minutes and reads for 35 minutes. How much time will he have left before his baseball practice? Explain.

Answer: He has no time left before his baseball practice.

Explanation:

Given, Paco has 75 minutes before he needs to get ready for baseball practice.

He cleans his room for 40 minutes and reads for 35 minutes.

40 + 35 = 75

75 = 75

The result is same , commutative property is used

So, He has no time left before his baseball practice.

Question 21.

**Mathematical PRACTICE 7 Identify Structure** Chloe ate 10 grapes and 5 crackers. Layla ate 5 grapes and 10 crackers. Who ate more food items? Write a number sentence. Then identify the property or rule used.

Answer: Chole and Layla , Both of them ate the food items equally

Explanation:

Given, Chloe ate 10 grapes and 5 crackers. Layla ate 5 grapes and 10 crackers.

Mathematically, we can write it as 10 + 5 and 5 + 10

Then, 10 + 5 = 5 + 10

15 = 15

The property used is Commutative Property

So, Chole and Layla , Both of them ate the food items equally

**HOT Problems**

Question 22.

**Mathematical PRACTICE 2 Use Number Sense** (23 + ) + 19 = 23 + + 19) Can any number complete the number sentence? Explain.

Answer: Yes , Having the same number on both the sides of the number sentence

Explanation:

For example, let the number be 5

( 23 + 5 ) + 19 = 23 + ( 5 + 19 )

47 = 47

As the property used here is Associative property , any number can complete the number sentence.

So, Yes , Having the same number on both the sides of the number sentence

Question 23.

**? Building on the Essential Question** How are addition properties and subtraction rules helpful when solving problems?

Answer:

The properties of addition and subtraction make it easier to work with numbers by allowing you to regroup them.

Explanation:

so that an equation is easier to solve. Understanding the properties of addition and subtraction can help you to work with numbers more effectively.

Addition determines the whole in terms of the parts, and subtraction determines a missing part.

### McGraw Hill My Math Grade 4 Chapter 2 Lesson 1 My Homework Answer Key

**Practice**

**Complete each number sentence. Identify the property or rule used.**

Question 1.

85 + 0 = ___

Answer: 85

Explanation:

For any number, zero plus that number is the number is called Identity property of addition

85 + 0 = 85

identity property is used

Question 2.

96 + 13 = 13 + ___

Answer: 109

Explanation:

The property which states that the order in which two numbers are added does not change the sum is Commutative property

96 + 13 = 13 + 96

Commutative property is used

Question 3.

____ – 0 = 37

Answer: 37

Explanation:

For any number, zero plus that number is the number is called Identity property of addition

37 – 0 = 37

Identity property is used.

Question 4.

(15 + 23) + 7 = 15 + (___ + 7)

Answer: 45

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

(15 + 23) + 7 = 15 + ( 23 + 7 )

45 = 45

Associative property is used.

**Problem Solving**

Question 5.

While bird watching, Gabrielle saw 6 robins and 3 blue jays. Chase saw 3 robins and 6 blue jays. Who saw more birds? Tell which property you used.

Answer: Both of them saw the birds equally

Explanation:

Given, Gabrielle saw 6 robins and 3 blue jays.

Chase saw 3 robins and 6 blue jays.

Mathematically, 6 + 3 and 3 + 6

6 + 3 = 3 + 6

Here , Commutative property is used

So, Both of them saw the birds equally

Question 6.

**Mathematical PRACTICE 5 Use Mental Math** For homework, Brooke has 15 math problems, 5 social studies problems, and 9 science problems. Use mental math to determine how many problems she has for homework. Tell which property you used.

Answer: Brooke has 29 problems altogether

Explanation:

Given, Brooke has 15 math problems, 5 social studies problems, and 9 science problems.

Using mental math,

15 + 5 + 9 = 29

Associative property is used here,

So, Brooke has 29 problems altogether

Question 7.

A soccer team scored 2 goals in the first half. If they won the game by a score of 2 goals to 1 goal, how many goals did they score in the second half? Tell which property you used.

Answer: They did not score any goals in the second half means 0 goals in the second half

Explanation:

Given, A soccer team scored 2 goals in the first half,

they won the game by a score of 2 goals to 1 goal,

The number sentence will be 2 + 0 = 2, As the team won the game by the score of 2 goals ,

Means they did not score any goals in the second half . that will the 0 goals in second half .

The property used here is identity property.

So, They did not score any goals in the second half means 0 goals in the second half.

**Vocabulary Check**

**Write a number sentence that demonstrates each property.**

Question 8.

Commutative Property of Addition ____

Answer: 48

Explanation:

The property which states that the order in which two numbers are added does not change the sum is Commutative property

24 +24 = 48

Commutative Property of Addition

Question 9.

Associative Property of Addition _____

Answer: 95

Explanation:

The property which states that the grouping of the addends does not change the sum is called Associative property.

19 + (61 + 15) = 95

Associative Property of Addition

Question 10.

Identity Property of Addition ____

Answer: 18

Explanation:

For any number, zero plus that number is the number is called Identity property of addition

0 + 18 = 18

Identity Property of Addition

**Test Practice**

Question 11.

Which number sentence represents the Commutative Property of Addition?

A. 357 + 0 = 357

B. (7+ 19) + 3 = 7 + (19 + 3)

C. 36 + 14 = 14 + 36

D. 79 – 79 = 0

Answer: C

Explanation:

The property which states that the order in which two numbers are added does not change the sum is Commutative property

36 + 14 = 14 + 36

50 = 50

The resultant will be same, even the place of thee number changes.

So, 36 + 14 = 14 + 36 , represents the Commutative Property of Addition.