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Study Guide6th GradeLevel 2 · Standard

Free 6th Grade Adding and Subtracting Fractions with Unlike Denominators

Walks through the method for adding and subtracting fractions when the denominators are different: find a common denominator, rename each fraction, then add or subtract the numerators. Includes answers bigger than one, mixed numbers and the most common mistakes.

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Grade
6th Grade
Subject
Math
Topic
Fractions
Difficulty
Level 2 · Standard
Estimated time
20 minutes
Curriculum
Texas grade levels (TEKS)
Answers
Not applicable
Format
PDF (A4) + print

Students will practice

  • understanding why fractions need a common denominator before adding
  • finding the lowest common denominator
  • adding and subtracting fractions with unlike denominators
  • converting improper fractions to mixed numbers

Curriculum: Texas grade levels (TEKS). We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Adding and Subtracting Fractions with Unlike Denominators

  1. 16th Grade Equivalent Fractions Worksheet — Level 1
  2. 26th Grade Equivalent Fractions Worksheet — Level 2
  3. 36th Grade Equivalent Fractions Worksheet — Level 3
  4. 46th Grade Simplifying Fractions Worksheet — Level 1
Study guide

How to use this study guide

  1. Read it together first, pausing at each worked example to try the step before reading the answer.
  2. Attempt the "Check yourself" questions at the end without looking back.
  3. Then practice with a worksheet from the pathway above and finish with the topic test.

Common questions

Who is this study guide for?

6th Grade students (typically ages 11–12) working on fractions. It is pitched at level 2 · standard.

Are the answers included?

This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.

How long does it take?

About 20 minutes. Short, regular sessions work best: two or three a week beats one long one.

Do I need to sign up to download?

No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.

What should we do next?

Try 6th Grade Equivalent Fractions Worksheet — Level 1.

Preview

Success TutoringWorksheets6th Grade · Mathematics · Fractions

Adding and Subtracting Fractions with Unlike Denominators

What you need to know

You can only add or subtract fractions when the pieces are the same size — that is, when the denominators are the same. If they are different, you first rename one or both fractions so they share a common denominator. Then you add or subtract the numerators and keep the denominator. Finally, simplify the answer if you can.

  1. Find the lowest common denominator (LCD): the smallest number both denominators divide into.
  2. Rename each fraction with that denominator (multiply top and bottom by the same number).
  3. Add or subtract the numerators. Keep the denominator.
  4. Simplify, and change an improper fraction to a mixed number if needed.

+

  1. LCD of 2 and 3 is 6.
  2. = and = .
  3. + = [frac 5/6].

−

  1. LCD of 4 and 6 is 12 (multiples of 4: 4, 8, 12; multiples of 6: 6, 12).
  2. = and = .
  3. − = [frac 7/12].

+

  1. 10 is a multiple of 5, so the LCD is 10 and only one fraction needs renaming.
  2. = .
  3. + = [frac 7/10].

+ (answer bigger than 1)

  1. LCD of 6 and 4 is 12.
  2. = and = .
  3. + = .
  4. 12 twelfths make 1 whole, with 7 twelfths left over: 1[frac 7/12].
DenominatorsMultiplesLCD
4 and 64, 8, 12 … and 6, 12 …12
3 and 53, 6, 9, 12, 15 … and 5, 10, 15 …15
2 and 88 is already a multiple of 28
6 and 96, 12, 18 … and 9, 18 …18
Common mistake: adding the denominators. + is not — two fifths is less than a half, so that answer cannot be right. The denominator only tells you the size of the pieces.
Multiplying the two denominators always gives a common denominator, but not always the lowest one. 4 × 6 = 24 works for quarters and sixths, but 12 is smaller and means less simplifying at the end.

1 + 2

  1. Add the whole numbers: 1 + 2 = 3.
  2. Add the fractions: = , so + = .
  3. Answer: 3[frac 3/4].

Check yourself

  1. + = ?
  2. − = ?
  3. + = ?
  4. − = ? (simplify)
  5. + = ? (as a mixed number)
  6. 1 + 1 = ?

Answers: 1. 2. 3. 4. = 5. = 1 6. 2 = 2

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Created by
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Last reviewed
1 October 2026
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