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Common Core Math5th GradeFractions

5.NF.1: Add and Subtract Fractions with Unlike Denominators

Also written as 5.NF.A.1 and CCSS.MATH.CONTENT.5.NF.A.1 · Cluster: Use equivalent fractions as a strategy to add and subtract fractions.

Make a 5.NF.1 WorksheetAll 26 5th Grade Math Standards

The Official Wording

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Common Core State Standards, Grade 5, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026

What 5.NF.1 Means in Plain English

Fifth graders add and subtract fractions whose denominators do not match, like 2/3 + 1/4. They rewrite both over a common denominator, here twelfths, so the sum is 8/12 + 3/12 = 11/12. Mixed numbers are included, which means regrouping a whole when the fraction parts pass 1.

Fourth grade added fractions only with like denominators (4.NF.3) and built equivalent fractions (4.NF.1). This standard joins the two ideas. The word problems come in 5.NF.2, and in 6th grade the same common-denominator thinking powers dividing fractions (6.NS.1).

5.NF.1 I Can Statements

  • I can find a common denominator for two fractions.
  • I can add and subtract fractions with unlike denominators.
  • I can add and subtract mixed numbers, regrouping when I need to.

5.NF.1 Worked Example

A board-cutting problem with fourths and thirds, where the fraction part has to borrow from a whole.

Problem

A board is 3 1/4 feet long. Jun cuts off 1 2/3 feet. How much board is left?

3 1/4 feet of board, minus 1 2/3 feet
  1. Fourths and thirds do not line up, so find a denominator both go into. 4 × 3 = 12 works.Common denominator: 12
  2. Rewrite each fraction part as twelfths. Multiply top and bottom by the same number so the value does not change.1/4 = 3/12, 2/3 = 8/12
  3. Now the problem is 3 3/12 − 1 8/12. You cannot take 8 twelfths from 3 twelfths, so borrow one whole from the 3 and turn it into 12/12.3 3/12 = 2 15/12
  4. Subtract the whole numbers and the fraction parts separately.2 − 1 = 1, 15/12 − 8/12 = 7/12
Answer1 7/12 feet of board left

Check it: Add it back: 1 7/12 + 1 2/3 = 1 7/12 + 1 8/12 = 2 15/12 = 3 3/12 = 3 1/4, the original length.

Common Mistakes with 5.NF.1

Adding the denominators

2/3 + 1/4 = 3/7

Try this: Show both fractions on a chart: 3/7 is smaller than 2/3 alone, so the sum cannot be 3/7. Denominators name piece size, not count.

Changing the bottom but not the top

1/4 = 1/12, so 2/3 + 1/4 = 8/12 + 1/12 = 9/12

Try this: Have students write the multiplier beside each fraction: 1/4 × 3/3 = 3/12. Whatever multiplies the denominator must multiply the numerator too.

Forgetting to regroup a mixed number

3 3/12 − 1 8/12 = 2 5/12 (subtracting 3 from 8 because it “works”)

Try this: Turn one whole into twelfths before subtracting: 3 3/12 becomes 2 15/12. Then 15/12 − 8/12 = 7/12 works without flipping anything.

Where 5.NF.1 Fits

Comes Before4.NF.1Make equivalent fractions, like 1/4 = 3/12, and explain why they match.4.NF.3Add and subtract fractions with like denominators, including mixed numbers.
Alongside5.NF.2Solve word problems with these sums and differences, and estimate to check.5.NBT.7Add and subtract decimals to hundredths, the same idea in base ten.
Comes Next6.NS.4Find the least common multiple of two numbers, the formal name for the smallest common denominator.6.NS.1Divide a fraction by a fraction, where common denominators appear again.

Practice 5.NF.1

Math Worksheet GeneratorFree ToolSums and differences with unlike denominators, mixed numbers included, with an answer key that shows the common denominator.FractionsUnlike denominatorsAnswer key
Make a Worksheet

Quick Check

  1. 2/3 + 1/4
  2. 5/6 − 1/2
  3. 2 1/2 + 1 2/3

5.NF.1: Other Names

5.NF.15.NF.A.1CCSS.MATH.CONTENT.5.NF.A.1

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.