Reducing Fractions Worksheets

Pick a level under Sheet type, from halving 6/8 to the 17 hidden in 51/85, then press Print.

12 problems. Lowest terms, denominators to 12. Sheet 57YIR7, with its answer key.

Lowest terms, denominators to 12

Name Date Score / 12

Write each fraction in lowest terms. Divide the numerator and the denominator by the same number until only 1 divides both.

  1. 1.210 = ________
  2. 2.68 = ________
  3. 3.212 = ________
  4. 4.610 = ________
  5. 5.412 = ________
  6. 6.26 = ________
  7. 7.36 = ________
  8. 8.28 = ________
  9. 9.312 = ________
  10. 10.48 = ________
  11. 11.46 = ________
  12. 12.912 = ________

Sheet 57YIR7 · Made at homeroomtools.com

Answer key. Lowest terms, denominators to 12

  1. 1.210 = 15 (top and bottom ÷ 2)
  2. 2.68 = 34 (top and bottom ÷ 2)
  3. 3.212 = 16 (top and bottom ÷ 2)
  4. 4.610 = 35 (top and bottom ÷ 2)
  5. 5.412 = 13 (top and bottom ÷ 4)
  6. 6.26 = 13 (top and bottom ÷ 2)
  7. 7.36 = 12 (top and bottom ÷ 3)
  8. 8.28 = 14 (top and bottom ÷ 2)
  9. 9.312 = 14 (top and bottom ÷ 3)
  10. 10.48 = 12 (top and bottom ÷ 4)
  11. 11.46 = 23 (top and bottom ÷ 2)
  12. 12.912 = 34 (top and bottom ÷ 3)

Sheet 57YIR7 · Made at homeroomtools.com

Next step Add unlike fractions, then reduce the answerSharpen the times tables behind factoring

How it works

Make reducing fractions worksheets at the level your class needs. The first sheet keeps denominators to 12. The Sheet type menu goes down to halving 6/8 and up to numbers such as 42/56. Press Make a new sheet for new fractions.

Read the full guide

A classroom convention, not a standard

The words lowest terms and simplest form appear nowhere in the Common Core or the Texas standards. How much credit 6/8 earns is your call. The standards do supply the tools. Equivalent fractions are in Common Core 4.NF.1 and Texas 4.3(C). The greatest common factor of two numbers up to 100 is in 6.NS.4.

Small steps, or one big one

24/36 can come down in steps, 24/36 = 12/18 = 6/9 = 2/3, or in one move by the greatest common factor, 12. Every route ends at the same fraction. Steps suit pupils still learning their factors. The GCF, which some books call the HCF, suits larger numbers: 42/56 = 3/4 takes one division by 14.

  • Start on Halve the top and the bottom: one halving finishes every fraction, so pupils fix the rule first.
  • Run Reduce or not? Mixed sheet before a test: about a quarter of its fractions are already in lowest terms.
  • Hundredths to lowest terms, with 75/100 = 3/4 and 5/100 = 1/20, is groundwork for decimals and percents.

Questions and answers

How do I know a fraction is in lowest terms?

When 1 is the only number that divides both the numerator and the denominator. In 4/9, the factors of 4 are 1, 2 and 4, and only 1 divides 9, so it is finished. A shortcut: a proper fraction over a prime denominator cannot reduce.

Is reducing the same as simplifying?

Yes. Reducing, simplifying and writing in lowest terms all mean dividing the numerator and the denominator by their common factors until only 1 is left. The value never changes: 12/18 and 2/3 sit at the same point on a number line.

What is the fastest way to reduce a fraction?

Divide both numbers by their greatest common factor: for 42/56 it is 14, and one division gives 3/4. If the GCF is hard to see, divide by any common factor and repeat. Most keys print the factor, as in top and bottom ÷ 14.

Do you reduce improper fractions and mixed numbers?

Yes, the same way. 18/12 = 3/2 after dividing both numbers by 6, and as a mixed number that is 1 1/2. In 3 6/8 only the fraction part changes, giving 3 3/4. Reducing before converting keeps the division small.

All 15 sheet types

Factors and the GCF 1

  • Reduce in one step with the GCF 24/36 = 2/3 in one move, because the greatest common factor is 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3. Pupils write the GCF in a box first, then divide once.

First steps, with help 4

  • Divide by the number shown 9/12 comes with ÷ 3 printed beside it: 9 ÷ 3 = 3 and 12 ÷ 3 = 4, so 9/12 = 3/4. The divisor is given, so pupils practice dividing both numbers before they have to find the factor themselves.
  • Fill in the reduced fraction's missing number 12/18 equals how many thirds? 18 ÷ 3 = 6, so both numbers were divided by 6, and 12 ÷ 6 = 2. The answer is 2/3. One number of the reduced fraction is printed and pupils find the other.
  • Halve the top and the bottom 6/8 = 3/4. Both numbers are even, so halve each one. On this sheet one halving always finishes the job, which makes it the gentlest way in.
  • Reduce to a unit fraction 4/12 = 1/3. When the numerator divides the denominator, the numerator is the greatest common factor and the answer has 1 on top. Pupils soon see it coming: 5/20, 3/18, 7/21.
Show all 15 sheet types (10 more)

Reduce to lowest terms 4

  • Lowest terms, denominators to 12 8/12 = 2/3, dividing both numbers by 4. Denominators are 4, 6, 8, 10 and 12: the ones on the Common Core grade 4 list, other than 100, whose proper fractions can reduce, since a proper fraction over 2, 3 or 5 never does.
  • Lowest terms, denominators to 24 15/24 = 5/8, dividing both numbers by 3. With denominators up to 24, common factors of 7 and 9 turn up beside the usual 2, 3 and 5, as in 14/21 = 2/3.
  • Reduce in steps 24/36 = 12/18 = 6/9 = 2/3. Halve, halve again, then divide by 3. Any common factor is a fair first move, and every route ends at the same fraction. The sheet leaves room for three steps.
  • Reduce or not? Mixed sheet 7/12 stays as it is, and 9/12 = 3/4. About a quarter of the fractions are already in lowest terms, so pupils have to check before they divide. The key writes in lowest terms already beside those.

Larger numbers and other methods 3

  • Hundredths to lowest terms 75/100 = 3/4, 40/100 = 2/5 and 5/100 = 1/20. These are the fractions behind 0.75, 0.40 and 0.05, so the sheet doubles as groundwork for decimals and percents. Texas 6.4(G) asks for equivalent forms of all three.
  • Numbers to 100 42/56 = 3/4. The greatest common factor is 14, and pupils who try small factors get there in two steps, 42/56 = 21/28 = 3/4. Both numbers stay at or below 100, the range Common Core 6.NS.4 sets for finding a GCF.
  • Tens and hundreds: cross off the zeros 30/40 = 3/4 and 300/500 = 3/5. Crossing one zero off the top and one off the bottom divides both numbers by 10. The sheet includes fractions such as 20/40 = 2/4 = 1/2, where the zeros go and a 2 is still left to divide out.

Improper fractions and mixed numbers 3

  • Improper fractions, left improper 18/12 = 3/2. Reducing works the same above 1: divide both numbers by 6 and stop. The answer stays improper, the form pupils will multiply and divide with later.
  • Reduce the fraction part of a mixed number 3 6/8 = 3 3/4. The whole number stays put and only the fraction part reduces. It is the last line of most mixed number sums, practiced here by itself.
  • Reduce, then write as a mixed number 18/12 = 3/2 = 1 1/2. Reducing first keeps the division small: 3 ÷ 2 is easier than 18 ÷ 12. The sheet has a box for each stage.

How this list was compiled: Own list of sheet types. Every worked example, greatest common factor and factor list was checked with exact arithmetic. Wording was checked against https://en.wikipedia.org/wiki/Fraction, https://en.wikipedia.org/wiki/Irreducible_fraction and https://en.wikipedia.org/wiki/Greatest_common_divisor. Standards were read in the full texts in September 2026: Common Core State Standards for Mathematics, https://learning.ccsso.org/wp-content/uploads/2022/11/Math_Standards1.pdf (4.OA.4, 4.NF.1 and the grade 4 footnote on denominators, 6.NS.4); Texas Essential Knowledge and Skills, 19 TAC chapter 111, https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf (4.3(C), 5.4(A)) and https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111b.pdf (6.4(G), 6.7(A)). Neither text uses the phrases lowest terms or simplest form. Licence: own work

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