Equivalent fractions chart
Equivalent fractions name the same amount: 1/2, 2/4 and 3/6 are all half. Multiply the numerator and the denominator by the same number and the fraction keeps its value. This chart does that for every fraction from halves to tenths.
Free printable PDF, 3rd grade to 5th grade.
One page, black and white, prints the same every time.
What is on the sheet
| Fraction | × 2 | × 3 | × 4 | × 5 | × 6 |
|---|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 5/10 | 6/12 |
| 1/3 | 2/6 | 3/9 | 4/12 | 5/15 | 6/18 |
| 2/3 | 4/6 | 6/9 | 8/12 | 10/15 | 12/18 |
| 1/4 | 2/8 | 3/12 | 4/16 | 5/20 | 6/24 |
| 3/4 | 6/8 | 9/12 | 12/16 | 15/20 | 18/24 |
| 1/5 | 2/10 | 3/15 | 4/20 | 5/25 | 6/30 |
| 2/5 | 4/10 | 6/15 | 8/20 | 10/25 | 12/30 |
| 3/5 | 6/10 | 9/15 | 12/20 | 15/25 | 18/30 |
| 4/5 | 8/10 | 12/15 | 16/20 | 20/25 | 24/30 |
| 1/6 | 2/12 | 3/18 | 4/24 | 5/30 | 6/36 |
| 5/6 | 10/12 | 15/18 | 20/24 | 25/30 | 30/36 |
| 1/8 | 2/16 | 3/24 | 4/32 | 5/40 | 6/48 |
| 3/8 | 6/16 | 9/24 | 12/32 | 15/40 | 18/48 |
| 5/8 | 10/16 | 15/24 | 20/32 | 25/40 | 30/48 |
| 7/8 | 14/16 | 21/24 | 28/32 | 35/40 | 42/48 |
| 1/10 | 2/20 | 3/30 | 4/40 | 5/50 | 6/60 |
| 3/10 | 6/20 | 9/30 | 12/40 | 15/50 | 18/60 |
| 7/10 | 14/20 | 21/30 | 28/40 | 35/50 | 42/60 |
| 9/10 | 18/20 | 27/30 | 36/40 | 45/50 | 54/60 |
Reading the chart
The first column is each fraction in its simplest form. Each column after it multiplies the top and the bottom by the number in its heading, so the 3/4 row reads 6/8, 9/12, 12/16, 15/20 and 18/24. Every fraction in a row is the same amount, the way 2 quarters and 4 eighths of a pizza are the same amount of pizza.
Read a row backwards to simplify: divide 9/12 by 3 on the top and the bottom and you are back at 3/4. To compare 2/3 and 3/4, look along both rows for the same denominator: 2/3 is 8/12 and 3/4 is 9/12, so 3/4 is bigger.
Where equivalent fractions come up
3rd grade explains equivalent fractions with models and number lines (CCSS 3.NF.A.3). 4th grade explains why multiplying the top and bottom works (4.NF.A.1), and 5th grade uses equivalent fractions to add and subtract fractions with unlike denominators (5.NF.A.1).
Common questions
- Why are there no fourths like 2/4 in the first column?
- The first column holds each fraction in simplest form. 2/4 is not simplest form; it is 1/2, and it appears in the halves row under × 2.
- Can I divide instead of multiply?
- Yes, as long as you divide the top and the bottom by the same number and both come out whole. That is how a fraction is simplified.