Adding and Subtracting Mixed Numbers Worksheet

Question 1

Find the sum: 2 1/4 + 1 2/4.

Accepted Answer

The sum is 3 3/4 because 2 + 1 = 3 and 1/4 + 2/4 = 3/4.

Question 2

Find the difference: 4 5/6 - 2 1/6.

Accepted Answer

The difference is 2 4/6, which simplifies to 2 2/3.

Question 3

Add: 3 1/2 + 2 1/4.

Accepted Answer

The sum is 5 3/4 because 1/2 equals 2/4, and 2/4 + 1/4 = 3/4.

Question 4

Subtract: 5 3/4 - 1 1/2.

Accepted Answer

The difference is 4 1/4 because 1 1/2 equals 1 2/4, and 5 3/4 - 1 2/4 = 4 1/4.

Question 5

Find the sum: 1 2/3 + 2 5/6.

Accepted Answer

The sum is 4 1/2 because 2/3 equals 4/6, so 1 4/6 + 2 5/6 = 3 9/6, which is 4 1/2.

Question 6

Find the difference: 6 1/5 - 3 4/5.

Accepted Answer

The difference is 2 2/5. Regroup 6 1/5 as 5 6/5, then subtract 3 4/5.

Question 7

A hiking trail is 2 3/8 miles long. A second trail is 1 5/8 miles long. How many miles long are the two trails altogether?

Accepted Answer

The two trails are 4 miles long altogether because 2 3/8 + 1 5/8 = 3 8/8, which equals 4.

Question 8

Mia has 3 1/2 cups of flour. She uses 1 3/4 cups. How much flour does she have left?

Accepted Answer

Mia has 1 3/4 cups of flour left because 3 1/2 equals 3 2/4, and 3 2/4 - 1 3/4 = 1 3/4 after regrouping.

Question 9

Which is greater: 2 1/3 + 1 2/3 or 3 1/4 + 1/4? Show your work.

Accepted Answer

The first sum is greater. 2 1/3 + 1 2/3 = 4, while 3 1/4 + 1/4 = 3 2/4, or 3 1/2.

Question 10

Subtract: 7 - 2 3/5.

Accepted Answer

The difference is 4 2/5. Regroup 7 as 6 5/5, then subtract 2 3/5.

Question 11

Add: 2 2/3 + 4 1/6.

Accepted Answer

The sum is 6 5/6 because 2/3 equals 4/6, and 4/6 + 1/6 = 5/6.

Question 12

Subtract: 8 1/4 - 3 5/8.

Accepted Answer

The difference is 4 5/8. Change 1/4 to 2/8, regroup 8 2/8 as 7 10/8, then subtract 3 5/8.

Question 13

Use a number line to add: 1 1/6 + 2 2/3.

Accepted Answer

The sum is 3 5/6 because 2 2/3 equals 2 4/6, and 1 1/6 + 2 4/6 = 3 5/6.

Question 14

A student says that 4 1/3 + 2 1/3 = 6 2/6. Explain the mistake and give the correct answer.

Accepted Answer

The mistake is adding the denominators. The denominators should stay the same because both fractions are thirds. The correct answer is 6 2/3.

Question 15

Write a story problem that can be solved with 5 1/2 - 2 3/4. Then solve it.

Accepted Answer

One possible story problem is: I had 5 1/2 yards of ribbon and used 2 3/4 yards. I have 2 3/4 yards left because 5 1/2 - 2 3/4 = 2 3/4.

Adding and Subtracting Mixed Numbers