Worksheets for Equivalent Fractions: Multiply Up, Divide Down

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12 problems. Find the missing numerator or denominator, factors 2 to 5. Sheet 9YGDFX, with its answer key.

Find the missing numerator or denominator, factors 2 to 5

Name Date Score / 12

Write the missing number that makes the two fractions equal. Whatever happens to the denominator has to happen to the numerator as well.

  1. 1.14 = 8
  2. 2.45 = 15
  3. 3.45 = 10
  4. 4.45 = 20
  5. 5.25 = 6
  6. 6.18 = 40
  7. 7.78 = 32
  8. 8.38 = 16
  9. 9.35 = 10
  10. 10.38 = 15
  11. 11.12 = 4
  12. 12.34 = 9

Sheet 9YGDFX · Made at homeroomtools.com

Answer key. Find the missing numerator or denominator, factors 2 to 5

  1. 1.14 = 28 (× 2)
  2. 2.45 = 1215 (× 3)
  3. 3.45 = 810 (× 2)
  4. 4.45 = 1620 (× 4)
  5. 5.25 = 615 (× 3)
  6. 6.18 = 540 (× 5)
  7. 7.78 = 2832 (× 4)
  8. 8.38 = 616 (× 2)
  9. 9.35 = 610 (× 2)
  10. 10.38 = 1540 (× 5)
  11. 11.12 = 24 (× 2)
  12. 12.34 = 912 (× 3)

Sheet 9YGDFX · Made at homeroomtools.com

Next step Use it: add unlike denominatorsMake a whole-number practice sheet

How it works

These worksheets for equivalent fractions open on twelve pairs such as 3/4 = 9/12 with one number left out, sometimes the top and sometimes the bottom. Sheet type has sheets that multiply up, divide down, and ask equal or not.

Read the full guide

One rule, two directions

Multiply the numerator and the denominator by the same number and the value stays the same: 2/3 = 8/12, both times 4. Dividing both works too: 6/8 = 3/4. Finding equivalent fractions worksheets drill that rule both ways, and the key prints the factor beside every line.

When no whole number fits

No whole number turns sixths into ninths. Neither denominator is a multiple of the other: 4/6 = 6/9 sends the pupil through lowest terms: both are 2/3. Grade 3 keeps to halves, thirds, fourths, sixths and eighths; Common Core adds fifths, tenths and twelfths in grade 4.

  • Start with Multiply by 2/2, 3/3 or 4/4: halves, thirds and fourths, where the factor is printed as a fraction equal to 1.
  • Equal or not? Halves, fourths and eighths shows whether a pupil sees 3/4 and 6/8 as one amount.

Questions and answers

How do you find an equivalent fraction?

Multiply or divide the numerator and the denominator by the same number: 1/2 = 2/4 = 4/8, and 10/15 = 2/3 when both are divided by 5. The value does not change, because the factor over itself equals 1.

What grade learns equivalent fractions?

Grades 3 and 4. Common Core 3.NF.3b asks for simple equivalents such as 1/2 = 2/4, and 4.NF.1 for the rule with any factor. Texas places them in 3.3(F) and 4.3(C).

Is there an equivalent fractions with models worksheet here?

Not on this page: these sheets are numbers only. For shaded circles and strips to name or shade, print the grade 3 fraction sheets.

Is there an answer key?

Yes. The key prints as the last page with each missing number filled in and the factor beside it, such as × 3 or ÷ 2. To leave it off, untick Answer key before you press Print.

All 14 sheet types

Find the missing number 4

  • Find the missing numerator or denominator, factors 2 to 5 The sheet the page opens on. One number of the second fraction is missing, sometimes the top and sometimes the bottom: 3/4 = 9/12, because 4 × 3 = 12 and 3 × 3 = 9. The key prints the factor beside each line.
  • Larger factors, 6 to 12: 3/8 = 21/56 The same missing-number lines with factors that need the times tables to 12: 3/8 = 21/56, because 8 × 7 = 56 and 3 × 7 = 21.
  • Missing denominator only: the new numerator is given The other way round: the factor comes from the numerators. 2/3 = 10/15, because 2 × 5 = 10 and 3 × 5 = 15.
  • Missing numerator only: the new denominator is given The pupil reads the factor off the two denominators and uses it on the numerator: 2/5 = 8/20, because 5 × 4 = 20 and 2 × 4 = 8. This is the step used later to rename a fraction over a common denominator.
Show all 14 sheet types (10 more)

Multiply the top and the bottom 2

  • Multiply by 2/2, 3/3 or 4/4: halves, thirds and fourths The factor is printed as a fraction equal to 1, so the pupil sees that nothing changes in value: 1/2 × 3/3 = 3/6. Only halves, thirds and fourths start the line, and the key prints the new fraction.
  • Write the whole equivalent fraction, factors 2 to 6 One problem to a line, with room to write. The line gives the fraction and the factor, 2/3 × 4/4, and the pupil writes both new numbers: 2/3 × 4/4 = 8/12.

Multiply up or divide down 5

  • Grade 3 denominators, missing numerator: 2/6 = 1/3 Halves, thirds, fourths, sixths and eighths only, the denominators both standards texts keep to in grade 3. A pair such as 3/6 and 2/4 has no whole-number factor between its sides, and the key says what both equal: 1/2.
  • Halves, fifths and tenths, up and down: 4/10 = 2/5 Tenths renamed as fifths or halves, and back again: 4/10 = 2/5 and 1/2 = 5/10. Useful before decimals, where 5/10 is written 0.5.
  • Halves, fourths and eighths, up and down: 6/8 = 3/4 Some lines multiply and some divide, and the key says which: 6/8 = 3/4 is top and bottom divided by 2, and 1/2 = 4/8 is both multiplied by 4. Dividing down is the first step toward lowest terms.
  • Neither denominator is a multiple of the other: 4/6 = 6/9 No whole number turns sixths into ninths, so the pupil goes through lowest terms: 4/6 and 6/9 are both 2/3. The key prints that fraction beside every line.
  • Thirds, sixths and twelfths, up and down: 4/12 = 1/3 The same in the thirds family: 4/12 = 1/3 divides both numbers by 4, and 2/3 = 8/12 multiplies both by 4.

Equal or not? 3

  • Equal or not? Halves to twelfths The same question with every denominator from 2 to 12 that grade 4 uses. One pair in three is equal, and the key gives both fractions one denominator: 3/5 and 6/10 are equal, because 3/5 = 6/10. An equal pair may be two names for one half, such as 2/4 and 5/10.
  • Equal or not? Halves, fourths and eighths The pupil writes <, > or = between two fractions; one pair in three is equal. The key renames one fraction so both have the same denominator: 3/4 and 6/8 are equal, because 3/4 = 6/8.
  • Equal or not? Neither denominator divides the other Fourths against sixths, sixths against ninths, tenths against fifteenths: no whole number turns one denominator into the other. For an equal pair the key prints the lowest terms of both sides: 4/6 and 6/9 are both 2/3.

How this list was compiled: The sheet types and the worked examples were written for this page, and every worked example was checked with exact fraction arithmetic by script on 2026-10-01. The rule behind every sheet (multiplying or dividing the numerator and the denominator by the same non-zero number gives an equivalent fraction) was read the same day at https://en.wikipedia.org/wiki/Fraction . Where the skill sits in school was read that day in the full text of the Common Core State Standards for Mathematics (California Department of Education copy, https://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf): 3.NF.3b (recognize and generate simple equivalent fractions such as 1/2 = 2/4 and 4/6 = 2/3), the grade 3 footnote that limits denominators to 2, 3, 4, 6 and 8, and 4.NF.1 (a/b is equivalent to (n × a)/(n × b)); and in the Texas Essential Knowledge and Skills for Mathematics (https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf): grade 3, 3.3(F) (equivalent fractions with denominators of 2, 3, 4, 6 and 8) and grade 4, 4.3(C) (determine if two given fractions are equivalent). Licence: own work

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