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Florida Grade 5 Math · Fractions

MA.5.FR.2.1: Adding and subtracting fractions

What this Grade 5 benchmark means, worked examples, common mistakes, and a free printable worksheet.

Created by a Florida mom · Published by Tropical Learning LLC

Download Free Worksheet (PDF)See worked examples

What Is Benchmark MA.5.FR.2.1?

In Grade 5, students learn to add and subtract fractions that have different denominators, such as 12 + 13. This also includes mixed numbers and fractions greater than 1.

The key idea: you can only add or subtract fractions when the pieces are the same size. So students first rewrite the fractions with a common denominator, then add or subtract the numerators.

Official benchmarkAdd and subtract fractions with unlike denominators, including mixed numbers and fractions greater than 1, with procedural reliability.

On the FAST test: part of the Grade 5 reporting category Number Sense and Operations with Fractions and Decimals, which is about 23–29% of the test.

Worked Examples

Worked Example 1

Adding Fractions

12 + 13
  1. 1Find a common denominator: 6.
  2. 2Rewrite 12 as 36.
  3. 3Rewrite 13 as 26.
  4. 4Add the numerators: 36 + 26 = 56.
Answer: 56

Worked Example 2

Subtracting Fractions

34 − 16
  1. 1Find a common denominator: 12.
  2. 2Rewrite 34 as 912.
  3. 3Rewrite 16 as 212.
  4. 4Subtract the numerators: 912 − 212 = 712.
Answer: 712

Worked Example 3

Adding Mixed Numbers

112 + 223
  1. 1Find a common denominator: 6.
  2. 2Rewrite as 136 + 246.
  3. 3Add the whole numbers and the fractions: 3 + 76.
  4. 4Regroup 76 as 116, so 3 + 116 = 416.
Answer: 416

Worked Example 4

Subtracting Mixed Numbers

313 − 156
  1. 1Find a common denominator: 6.
  2. 2Rewrite as 326 − 156.
  3. 326 is less than 56, so regroup one whole: 326 = 286.
  4. 4Subtract: 286 − 156 = 136.
  5. 5Simplify: 136 = 112.
Answer: 112

Common Mistakes to Watch For

Adding the denominators

Wrong:12 + 13 = 25

Denominators tell the size of the pieces, so they are never added. Rewrite with a common denominator first: 36 + 26 = 56.

Changing the denominator but not the numerator

Wrong:12 = 16

Whatever you multiply the denominator by, multiply the numerator by the same number: 12 = 36.

Subtracting backward instead of regrouping

Wrong:326 − 156 = 236

When the top fraction is smaller, borrow one whole: 326 becomes 286. Then subtract.

Leaving a fraction greater than 1 in a mixed number

Wrong:3 + 76 = 376

Regroup 76 as 116 and add the whole: 416.

Helpful Math Tip

Estimate before you calculate. 12 + 13 is a little less than 1, so an answer like 25 cannot be right. Checking whether an answer makes sense catches most mistakes.

Related Grade 5 Skills

MA.5.FR.2.2

Multiplying fractions

MA.5.AR.1.2

Fraction word problems

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Independent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.