These 25 PDF worksheets work on a single idea: two fractions are equivalent when you get from one to the other by multiplying or dividing the numerator and denominator by the same number. Each worksheet has its own answer key as a separate file. To understand the method before practicing, the equivalent fractions calculator explains it with another example and generates the list of equivalents of any fraction.
Which worksheet to choose
Choose the type of problem first and then the level. There are four types: find the missing numerator, find the missing denominator, decide whether two fractions are equivalent (yes or no) and mixed. The level sets the size of the denominators. In level 1 the starting fraction goes up to denominator 10 and the equivalent one to 30, in level 2 to 12 and 36, in level 3 to 20 and 60, and in level 4 to 30 and 120.
| Type | Levels 1 and 2 | Levels 3 and 4 |
|---|---|---|
| Find the missing numerator | Level 1: 12. Level 2: 12 and 20 | Level 3: 12 and 16. Level 4: 12 |
| Find the missing denominator | Level 1: 12. Level 2: 12 and 20 | Level 3: 12. Level 4: 12 |
| Yes or no | Level 1: 12. Level 2: 12 and 8 | Level 3: 12 and 8. Level 4: 12 |
| Mixed | Level 1: 12 and 20. Level 2: 12 and 20 | Level 3: 12 and 20. Level 4: 12 and 20 |
The 8- and 12-problem worksheets work as a warm-up or an exit ticket for a class, the 16-problem ones as intermediate practice and the 20-problem ones as extra practice. A 12-problem worksheet with no mistakes is a good sign to move on to the same type at the next level.
A test problem with two parts
A typical level 3 problem asks for two things in a row: complete a fraction and use that result to decide about another.
Worked example: two boards
A board is 7/12 of a yard long. a) Write that length in sixtieths of a yard. b) Another board is 21/36 of a yard long. Are the two the same length?
- Find the factor. To go from 12 to 60 you multiply by 5, because 60 ÷ 12 = 5.
- Multiply both terms by 5. 7 × 5 = 35 and 12 × 5 = 60, so 7/12 = 35/60.
- Cross-multiply for part b. 7 × 36 = 252 and 12 × 21 = 252. The products match.
Final result: a) 35/60 of a yard and b) yes, the two boards are the same length.
Check. Dividing 21/36 by 3 and 35/60 by 5 gives 7/12 in both cases.
A good solution shows the factor, says that you multiply top and bottom, and names the unit. Writing down the factor is enough for the teacher to see that the student did not guess.
Where students go wrong most
The most repeated mistake is thinking in terms of addition instead of multiplication. It seems reasonable because going from 2/3 to 4/5 raises both terms by 2, but the value changes.
A variant shows up on the missing denominator worksheets: working out the difference between numerators. In 3/5 = 12/?, some students subtract 12 − 3 = 9 and write 5 + 9 = 14. The factor is 12 ÷ 3 = 4 and the denominator is 5 × 4 = 20. The yes-or-no worksheet also helps with this mistake, because it makes the student test the whole pair before answering.
Five problems to try before printing
- Complete: 4/9 = ?/45.
- A tank is filled to 3/5 of its height. An identical tank has its height marked with 20 equal lines. Up to which line does the water reach if the level is the same?
- Are 6/16 and 9/24 equivalent? Justify your answer.
- Complete 2/7 = 10/? and then decide whether 14/49 is also equivalent to 2/7.
- Ana has walked 3/8 of a trail, which equals 15 segments of the same length. Into how many segments is the whole trail divided?
Show the answers
- 20/45, because 45 ÷ 9 = 5 and 4 × 5 = 20
- Up to line 12, since 3/5 = 12/20
- Yes, because 6 × 24 = 144 and 16 × 9 = 144, and both reduce to 3/8
- 10/35, because the factor is 5. And 14/49 is too, because 7 × 7 = 49 and 2 × 7 = 14
- 40 segments, because 3/8 = 15/40 with factor 5
For teachers
Before asking for cross products, let the student see with paper strips that 1/2 and 2/4 take up the same space; the coloring and drawing worksheets help with that visual step. With a mixed group, hand out “find the missing numerator” to whoever is starting and “yes or no” to whoever is moving ahead. When the student has to find a missing term in any position, the missing fraction value calculator solves the whole equation.
To practice with automatic feedback, there is fraction practice. After this series, the simplify fractions worksheets go the opposite way, and the compare and order fractions ones use equivalent fractions to bring fractions to the same denominator. If you need other numbers, the fraction worksheet generator creates a new sheet, and the fraction worksheet index gathers the other topics.
Sources
The Common Core State Standards Initiative page Grade 4, Number and Operations in Fractions lists standard 4.NF.A.1: explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models (consulted October 17, 2026).