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Order of Operations with Fractions

Evaluate Exponents

Multiply and divide

Add and Substract

Order of Operations with Fractions

Evaluate Exponents

Multiply and divide

Add and Substract

1.
MAT 040: Basic Math Learning Unit 6: Handout

Order of Operations with Fractions

Order of Operations

1. Do all operations inside parentheses and other grouping symbols.

2. Evaluate exponents.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.

Example 1

Solve. There are no operations inside parentheses so

evaluate the exponents first.

Multiply next.

Always multiply before adding or subtracting.

Now subtract. Remember to get a common

denominator when subtracting.

Answer:

Example 2

Solve. There are no operations inside parentheses so

evaluate the exponents first.

Multiply next.

Always multiply before adding or subtracting.

Find a common denominator

Add the fractions.

Answer:

Page 1 of 6

Order of Operations with Fractions

Order of Operations

1. Do all operations inside parentheses and other grouping symbols.

2. Evaluate exponents.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.

Example 1

Solve. There are no operations inside parentheses so

evaluate the exponents first.

Multiply next.

Always multiply before adding or subtracting.

Now subtract. Remember to get a common

denominator when subtracting.

Answer:

Example 2

Solve. There are no operations inside parentheses so

evaluate the exponents first.

Multiply next.

Always multiply before adding or subtracting.

Find a common denominator

Add the fractions.

Answer:

Page 1 of 6

2.
MAT 040: Basic Math Learning Unit 6: Handout

Example 3

Solve. Perform operations inside parentheses first.

Find a common denominator when

adding fractions.

Now add and subtract from left to right.

Find a common denominator for all

the denominators.

Answer:

Example 4

Solve. Multiply and divide from left to right.

When dividing, invert and multiply.

Add and subtract from left to right.

Get a common denominator.

Answer:

Page 2 of 6

Example 3

Solve. Perform operations inside parentheses first.

Find a common denominator when

adding fractions.

Now add and subtract from left to right.

Find a common denominator for all

the denominators.

Answer:

Example 4

Solve. Multiply and divide from left to right.

When dividing, invert and multiply.

Add and subtract from left to right.

Get a common denominator.

Answer:

Page 2 of 6

3.
MAT 040: Basic Math Learning Unit 6: Handout

Example 5

Solve. Always multiply before adding or subtracting.

Find a common denominator when

subtracting fractions.

Answer:

Example 6

Solve. Always divide before adding or subtracting.

When dividing, invert and multiply.

Get a common denominator when

subtracting fractions.

Answer:

Example 7

Multiply before adding or subtracting.

Add or subtract from left to right.

Get a common denominator when subtracting.

Get a common denominator when adding.

Reduce.

Answer:

Page 3 of 6

Example 5

Solve. Always multiply before adding or subtracting.

Find a common denominator when

subtracting fractions.

Answer:

Example 6

Solve. Always divide before adding or subtracting.

When dividing, invert and multiply.

Get a common denominator when

subtracting fractions.

Answer:

Example 7

Multiply before adding or subtracting.

Add or subtract from left to right.

Get a common denominator when subtracting.

Get a common denominator when adding.

Reduce.

Answer:

Page 3 of 6

4.
MAT 040: Basic Math Learning Unit 6: Handout

Example 8

Perform operations inside the parentheses first.

Get a common denominator when

adding fractions.

Next evaluate the exponents.

Next multiply before adding or subtracting.

Get a common denominator when adding or

subtracting fractions.

Next add or subtract from left to right.

Page 4 of 6

Example 8

Perform operations inside the parentheses first.

Get a common denominator when

adding fractions.

Next evaluate the exponents.

Next multiply before adding or subtracting.

Get a common denominator when adding or

subtracting fractions.

Next add or subtract from left to right.

Page 4 of 6

5.
MAT 040: Basic Math Learning Unit 6: Handout

Example 9

The following rainfall amounts were recorded: June inches, July inches, August inches and

September inches. Find the average rainfall for the four months.

To find the average amount of rainfall in this problem, add the numbers and divide by the

number of numbers. So you will add the four numbers and divide by 4.

+

__________

13

Now divide this sum by 4.

The average rainfall is inches.

Answer:

Page 5 of 6

Example 9

The following rainfall amounts were recorded: June inches, July inches, August inches and

September inches. Find the average rainfall for the four months.

To find the average amount of rainfall in this problem, add the numbers and divide by the

number of numbers. So you will add the four numbers and divide by 4.

+

__________

13

Now divide this sum by 4.

The average rainfall is inches.

Answer:

Page 5 of 6

6.
MAT 040: Basic Math Learning Unit 6: Handout

Example 10

Bob weighed pounds, Bill weighed and John weighed pounds.

Find the average weight for the three boys.

To find the average weight in this problem, add the numbers and divide by the number of

numbers. So you will add the three numbers and divide by 3.

___________

487

Now divide this sum by 3.

The average weight is pounds

Answer:

© Brenda Moore and Indian Hills Community College

Page 6 of 6

Example 10

Bob weighed pounds, Bill weighed and John weighed pounds.

Find the average weight for the three boys.

To find the average weight in this problem, add the numbers and divide by the number of

numbers. So you will add the three numbers and divide by 3.

___________

487

Now divide this sum by 3.

The average weight is pounds

Answer:

© Brenda Moore and Indian Hills Community College

Page 6 of 6