Name Date
Equivalent fractions worksheets
Write the number that makes each pair of fractions equal.
1.
15
2.
16
3.
57
4.
710
5.
34
6.
45
7.
78
8.
25
9.
25
10.
27
11.
711
12.
35
13.
910
14.
12
15.
16
16.
17
17.
910
18.
1112
19.
14
20.
310
Equivalent fractions worksheets
Fill in the missing number that makes two fractions equal, with the gap in the numerator, the denominator or either, and the scale factor kept sensible.
Grade 3–Grade 6 · every refresh draws a new set · answer key included
Equivalent fractions worksheets — answer key
Write the number that makes each pair of fractions equal.
1.
15=
2.
16=
3.
57=
4.
710=
5.
34=
6.
45=
7.
78=
8.
25=
9.
25=
10.
27=
11.
711=
12.
35=
13.
910=
14.
12=
15.
16=
16.
17=
17.
910=
18.
1112=
19.
14=
20.
310=
20 problems · US Letter · answer key — 2 sheets, page breaks marked in the preview
What this worksheet is for
Two fractions are equivalent when they name the same amount written with different numbers, and the whole idea rests on one rule: multiply the top and the bottom by the same thing and nothing changes. These questions show one fraction complete and the other with a gap, so the pupil has to work out the scale factor and then apply it. It is the same skill that turns unlike denominators into like ones a year later, which is the real reason it is worth drilling.
Who it suits
Grade 3 to Grade 6, ages eight to twelve. It sits between naming fractions and adding them, and it is the topic to return to whenever a class struggles with common denominators later on.
How to use the settings
Start with the gap in the numerator — the pupil sees both denominators, works out what one was multiplied by, and applies it upward. A gap in the denominator is harder, because the scale factor has to be deduced from the numerators. Either mixes the two and is the right setting once both directions are secure.
What goes wrong
Adding the same number to both parts instead of multiplying is the misconception this page exists to expose: from one half a pupil writes two thirds, which is wrong but follows a rule they have invented. The other error is applying the scale factor in the wrong direction when the second fraction is the smaller one.
Questions
- Why can I multiply the top and bottom but not add to them?
- Because multiplying both by the same number is multiplying by one in disguise — two over two is one, and multiplying by one changes nothing. Adding two to both parts is not multiplying by anything, so it changes the value.
- Is the first fraction always in lowest terms?
- Yes, which is what makes the scale factor unambiguous and keeps the numbers small.
- How does this connect to adding fractions?
- Finding a common denominator is exactly this skill: rewriting one or both fractions as an equivalent fraction with the denominator you need. A class that is fluent here finds common denominators easily.