MathPractice
Fractions · Grade 5

Add and subtract unlike fractions

Rename different-sized parts before combining them. A common denominator lets you count parts of the same size.

Grade 58 questions per setNo account needed
Practice 8 questions Download worksheet

US Letter PDF · A4 version · Answer key

What we’re working onAdd and subtract unlike fractions and use an estimate to check the result.

First page of the Add and subtract unlike fractions worksheet, with visible questions and room to work.Open worksheet PDF · 8 questions · US Letter
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Worked examples

Example 1

Add thirds and fourths

Find 1/3 + 1/4.

  1. Thirds and fourths are different-sized parts. Split the same whole into twelfths.
  2. One third is 4/12, and one fourth is 3/12.
  3. Add the twelfths: 4/12 + 3/12 = 7/12. The sum is between one half and one.

1/3 + 1/4 = 7/12

Example 2

Subtract fourths from sixths

Find 5/6 − 1/4.

  1. Use twelfths as the shared part size.
  2. Five sixths is 10/12, and one fourth is 3/12.
  3. Subtract: 10/12 − 3/12 = 7/12. This is less than 5/6, as a positive amount was removed.

5/6 − 1/4 = 7/12

A question from this worksheet

Find 7/8 − 5/10.

See the explanation

3/8

7/8 − 5/10 = 35/40 − 20/40 = 3/8.

Choose how to practice

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Each set has eight questions. The online practice and prepared worksheet use the same questions.

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For the grown-up beside them

Help the thinking along.

A useful question

What equal-size pieces could represent both fractions? How will each numerator change?

What to look for

The learner renames both fractions accurately, performs the operation on numerators, and checks the size of the result.

A common sticking point

Changing a denominator without changing its numerator, or adding the original denominators.

Help without giving the answer

Align two equal-length bars. Split each into a part size that fits both original partitions, then recount the selected parts.

Keep the words clear

Words in this skill.

unlike denominators
Denominators that differ.
common denominator
A denominator that can be used to rename both fractions with equal-size parts.
least common denominator
The smallest positive denominator that both fractions can be renamed with.
equivalent fractions
Fractions that keep the same value while using different names.

What these sets cover.

  • Use denominators 2 to 12, with least common denominator no greater than 60.
  • Start where one denominator divides the other, then use pairs needing a new denominator.
  • Subtraction results stay nonnegative. Equivalent student answers are not restricted to the generator denominator list.

Common questions

Must I choose the least common denominator?

No. Another common denominator can work. The least one often keeps the numbers smaller. Equivalent final answers are accepted unless the task requests a form.

Why is 1/3 + 1/4 not 2/7?

A third and a fourth are different-sized pieces. Count equal-size pieces instead: they become four twelfths and three twelfths, totaling seven twelfths.

Try next

Mixed numbers: unlike denominators

Next, combine this common-denominator method with whole numbers and regrouping.

Explore this skill

Related standards: 5.NF.1. These materials focus on this skill, not every part of a grade-level curriculum. How we check materials.