## Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract

**Using Mental Math to Add and Subtract**

How can you use mental math to add and subtract?

Properties can sometimes help you add using mental math. How many years have Ms. Walston and Mr. Randall been teaching? What is the total number of years all of the teachers in the chart have been teaching?

Other Examples

Add using mental math.

Find 135 + 48.

Use breaking apart to find a ten.

Adding 5 to 135 is easy. Break apart 48.

135 + 5 = 140

140 + 43 = 183

So, 135 + 48 = 183.

Use compensation.

135 + 48

135 + 50 = 185

Think I added 2 too many,

so I will subtract 2.

185 – 2 = 183

So, 135 + 48 = 183.

Subtract using mental math.

Find 400 – 165.

Use counting on.

165 + 5 = 170

170 + 30 = 200

200 + 200 = 400

5 + 30 + 200 = 235

So, 400 -165 = 235.

Use compensation.

Find 260 – 17.

It is easy to subtract 20.

260 – 20 = 240

Think I subtracted 3 too many,

so I will add 3.

240 + 3 = 243

So, 260 – 17 = 243.

Commutative Property of Addition

You can __add two numbers in any order.__

Ms. Walston and Mr. Randall have been teaching a combined total of 42 years.

Associative Property of Addition

You can __change the grouping of addends.__

The total number of years the three teachers have been teaching is 47 years.

Identity Property of Addition

__Adding zero does not change the number.__

12 + 0 = 12

**Guided Practice***

Do You Know how?

In 1 through 6, use mental math to add or subtract.

Question 1.

86 + 25

Answer:

Question 2.

497 + 0

Answer:

Question 3.

566 – 359

Answer:

Question 4.

169 – 48

Answer:

Question 5.

239 + 509

Answer:

Question 6.

(40 + 5) + 8

Answer:

Do You Understand?

Question 7.

How could you use compensation to find 391 – 26?

Answer:

Question 8.

Writing to Explain Explain how you used mental math to find the answer to Exercise 4.

**Independent Practice**

Leveled Practice In 9 through 18, use mental math to complete the calculation.

Question 9.

400 – 227

Answer:

Question 10.

500 – 89

Answer:

Question 11.

906 – 289

Answer:

Question 12.

7,000 + 2,130

Answer:

Question 13.

583 + 317

Answer:

Question 14.

125 + 28

Answer:

Question 15.

1,700 – 315

Answer:

Question 16.

2,000 + 4,996

Answer:

Question 17.

438 – 129

Answer:

Question 18.

0 + 284

Answer:

**Problem Solving**

For 19 through 21 , use the table to the right.

Question 19.

Which state has the greatest land area in square miles?

Answer:

Question 20.

Which two states shown in the table have the smallest difference in land area?

Answer:

Question 21.

Which two states shown in the table have the greatest difference in land area?

Answer:

Question 22.

Colin had 148 CDs in his collection. He traded 32 of them for 23 that he really wanted. How many CDs does Colin now have in his collection? Use mental math.

A. 106 CDs

B. 108 CDs

C. 116 CDs

D. 139 CDs

Answer:

Question 23.

Ms. Gomez’s class collected pencils for the community school supplies drive. Ethan’s group brought in 143 pencils and Marcelina’s group added 78 more. How many pencils did the groups contribute altogether?

A. 184 pencils

B. 204 pencils

C. 221 pencils

D. 245 pencils

Answer:

Question 24.

Number Sense Is 881 – 262 more or less than 500? Explain how you can tell using mental math.

Answer:

Question 25.

Writing to Explain How can you use mental math to subtract 158 – 29?

Answer:

Question 26.

An adult human body has a total of 206 bones. There are 300 bones in a child’s body because some of a child’s bones fuse together as a child grows. How many more bones are in a child’s body than in an adult’s body?

Answer:

Question 27.

Number Sense Write two numbers that have a 6 in the ones place and an 8 in the hundreds place.

Answer:

**Algebra Connections**

Solving Number Sentences with Addition and Subtraction

A number sentence uses the equal sign (=) to show that two expressions have the same value. Fill in the box in each number sentence with the whole number that makes the number sentence true. Check your answers.

Example:

Think What number plus 8 equals 35?

When solving an addition number sentence, use subtraction to identify the missing number.

Think What is 35 minus 8?

Subtract 8 from 35.

35 – 8 = 27

Now, add 8 and 27.

8 + 27 = 35

Copy and complete each number sentence.

Question 1.

7 + = 31

Answer:

Question 2.

+ 6 = 21

Answer:

Question 3.

26 – = 25

Answer:

Question 4.

56 – = 38

Answer:

Question 5.

– 47 = 12

Answer:

Question 6.

66 + = 85

Answer:

Question 7.

– 98 = 1

Answer:

Question 8.

103 – = 72

Answer:

Question 9.

10 + = 13

Answer:

Question 10.

– 8 = 12

Answer:

Question 11.

1 + = 7

Answer:

Question 12.

744 – = 327

Answer:

For 13 through 16, copy and complete the number sentence below each problem. Use it to help explain your answer.

Question 13.

Cheryl made 8 free-throw shots. She shot a total of 10 free-throw shots. How many free-throw shots did she miss?

8 + = 10

Question 14.

7 rabbits less than a certain number of rabbits is 13 rabbits. What is the value of the variable?

– 7 = 13

Answer:

Question 15.

George delivered 118 newspapers in two days. He delivered 57 newspapers the first day. How many newspapers did George deliver the second day?

57 + = 118

Answer:

Question 16.

The cost of an apple is 39¢. Robert had 25¢ in his pocket. How much more money did Robert need to purchase the apple?

25 + = 39

Answer: