Decomposing Fractions Worksheets

Choose a split in Sheet type, from 5/6 as five unit fractions to 7/8 in three parts, then press Print.

12 problems. Two different splits of one fraction. Sheet E91HK3, with its answer key.

Two different splits of one fraction

Name Date Score / 12

Split each fraction into two parts with the same denominator, in two different ways. There is more than one right answer: the key shows one, and any parts that add up to the fraction are right.

  1. 1.710 = _____ + _____710 = _____ + _____
  2. 2.412 = _____ + _____412 = _____ + _____
  3. 3.712 = _____ + _____712 = _____ + _____
  4. 4.56 = _____ + _____56 = _____ + _____
  5. 5.1012 = _____ + _____1012 = _____ + _____
  6. 6.912 = _____ + _____912 = _____ + _____
  7. 7.910 = _____ + _____910 = _____ + _____
  8. 8.510 = _____ + _____510 = _____ + _____
  9. 9.78 = _____ + _____78 = _____ + _____
  10. 10.610 = _____ + _____610 = _____ + _____
  11. 11.812 = _____ + _____812 = _____ + _____
  12. 12.810 = _____ + _____810 = _____ + _____

Sheet E91HK3 · Made at homeroomtools.com

Answer key. Two different splits of one fraction

  1. 1.710 = 110 + 610 (one way of many)710 = 210 + 510
  2. 2.412 = 112 + 312 (one way of many)412 = 212 + 212
  3. 3.712 = 112 + 612 (one way of many)712 = 212 + 512
  4. 4.56 = 26 + 36 (one way of many)56 = 16 + 46
  5. 5.1012 = 312 + 712 (one way of many)1012 = 412 + 612
  6. 6.912 = 412 + 512 (one way of many)912 = 212 + 712
  7. 7.910 = 410 + 510 (one way of many)910 = 310 + 610
  8. 8.510 = 210 + 310 (one way of many)510 = 110 + 410
  9. 9.78 = 18 + 68 (one way of many)78 = 28 + 58
  10. 10.610 = 310 + 310 (one way of many)610 = 110 + 510
  11. 11.812 = 112 + 712 (one way of many)812 = 212 + 612
  12. 12.810 = 310 + 510 (one way of many)810 = 410 + 410

Sheet E91HK3 · Made at homeroomtools.com

Next step Make a whole-number worksheet

All 5 sheet types

Into unit fractions 1

  • Split into unit fractions 5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6. The numerator says how many unit fractions to write and the denominator says which one. Denominators are 3, 4, 6 and 8, and no fraction passes one whole, the numerator limit of 3.3(D).

Into two parts 2

  • Split 1 whole into two fractions 1 = 8/8 = 3/8 + 5/8. One part is given and the pupil finds the part that finishes the whole. It is the fraction form of making ten, and it is the fact pupils need before they can add past 1.
  • Split in two, one part given One part is printed and the pupil finds the other. For 7/10 with 3/10 given, the missing part is 4/10, because 7/10 = 3/10 + 4/10. It is a missing addend problem on the numerators alone.

More than one way 2

  • Split into three parts 7/8 = 1/8 + 2/8 + 4/8, or 2/8 + 2/8 + 3/8, or any three fractions whose numerators add to 7. Pupils write one three-part sum for each fraction. Three parts is where pupils stop guessing and start treating the numerator as a number to break up.
  • Two different splits of one fraction 5/6 = 1/6 + 4/6 = 2/6 + 3/6. Each problem has room for two sums, and swapping the order of the parts does not count as a new one. This is the sheet that Common Core 4.NF.3b and Texas 4.3(B) describe: more than one way, each written as an equation.

How it works

Make decomposing fractions worksheets for the grade 4 skill of writing one fraction as a sum. Sheet type runs from 5/6 as five unit fractions to 7/8 in three parts. Make a new sheet changes the fractions.

Read the full guide

A kindergarten idea with a denominator

Common Core K.OA.3 has kindergarten pupils break a number into pairs in more than one way, 5 = 2 + 3 and 5 = 4 + 1. Grade 4 standard 4.NF.3b asks for the same thing with a denominator attached: 5/8 = 2/8 + 3/8 and 5/8 = 4/8 + 1/8. Texas 4.3(B) matches it, and 3.3(D) starts a year earlier with sums of unit fractions.

A key for many right answers

7/8 can be 1/8 + 6/8, 2/8 + 5/8 or 3/8 + 4/8, and a pupil who writes any of them is correct. The key prints one sample answer, marked one way of many. To check any other, the denominator stays and the numerators add to the one you started with.

  • Use Split 1 whole into two fractions before adding past 1. Pupils who know that 3/8 needs 5/8 can make a whole first.

Questions and answers

What does decomposing a fraction mean?

Writing it as a sum of smaller fractions with the same denominator. 3/4 can be 1/4 + 1/4 + 1/4 or 1/4 + 2/4. The smallest pieces are unit fractions, which have a numerator of 1.

Should the parts be reduced to lowest terms?

Not on these sheets. 6/8 = 2/8 + 4/8 is a finished answer, and rewriting the parts as 1/4 and 1/2 hides the fact that the numerators add to 6.

Do the sheets come with answers?

Yes. Page 2 is the answer key. Where many answers are right it shows one, and the line under the sheet's title says how to check others. To keep a copy, press Print and choose Save as PDF. Both pages carry the same sheet code.

More tools

Show 6 more

Browse Math