Equivalent Fractions: Chart, Rules And Examples
The short version
- Equivalent fractions are different fractions that name the same amount. 1/2, 2/4, 3/6 and 50/100 are all equal.
- To make an equivalent fraction, multiply or divide the numerator and denominator by the same number (not zero). 3/5 × 3/3 = 9/15.
- To check whether two fractions are equivalent, cross multiply. 4/6 and 6/9 match because 4 × 9 = 36 and 6 × 6 = 36.
- Kids need this skill to compare fractions, add fractions with different denominators, and simplify answers, so a shaky grasp here shows up for years.
Equivalent fractions are fractions that look different but stand for the same value. Half a pizza is the same amount whether you cut it into 2 slices and take 1, or cut it into 8 slices and take 4, so 1/2 = 4/8. You find them by multiplying or dividing the top and bottom of a fraction by the same number.
Below you’ll find the rule, why it works, an equivalent fractions chart, how to test two fractions, and practice with answers.
Why multiplying top and bottom works
Any number over itself equals 1. 2/2 = 1, 5/5 = 1, 100/100 = 1. And multiplying by 1 never changes a value. So when you do this:
1/2 × 3/3 = 3/6
you haven’t changed the amount at all. You’ve just cut the same whole into more, smaller pieces. The whole now has 6 pieces instead of 2, and you have 3 of them instead of 1. Same amount of pizza.
Dividing works for the same reason, just in reverse. 8/12 ÷ 4/4 = 2/3. You’re grouping small pieces into bigger ones.
This is also why adding the same number to the top and bottom doesn’t work. 1/2 becomes 2/3 if you add 1 to each, but 2/3 is bigger than a half. Adding changes the value. Multiplying by a form of 1 doesn’t.
How to find equivalent fractions
Method 1: multiply to build up
Pick any whole number and multiply both parts by it.
3/5 × 2/2 = 6/10
3/5 × 3/3 = 9/15
3/5 × 4/4 = 12/20
Every fraction has infinitely many equivalent fractions, because you can always pick a bigger multiplier.
Method 2: divide to simplify
Find a number that divides both the numerator and denominator evenly. The biggest one, the greatest common factor, gets you to simplest form in one step.
Simplify 18/24.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Greatest common factor: 6
18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 = 3/4
If you don’t spot the biggest factor, smaller steps work too: 18/24 ÷ 2/2 = 9/12, then 9/12 ÷ 3/3 = 3/4. Just keep going until nothing else divides both.
Method 3: find a missing number
Worksheets love this one: 2/3 = ?/12.
Ask what the denominator was multiplied by: 3 × 4 = 12.
Do the same to the numerator: 2 × 4 = 8.
So 2/3 = 8/12.
It works in either direction. For 5/8 = 20/?, the top went from 5 to 20, which is × 4. So the bottom is 8 × 4 = 32.
Equivalent fractions chart
Each row shows a fraction, four of its equivalent fractions, and its decimal. The decimal column is handy when you need the fractional equivalent of a decimal, or the reverse.
| Fraction | × 2 | × 3 | × 4 | × 5 | Decimal |
|---|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 5/10 | 0.5 |
| 1/3 | 2/6 | 3/9 | 4/12 | 5/15 | 0.333… |
| 2/3 | 4/6 | 6/9 | 8/12 | 10/15 | 0.666… |
| 1/4 | 2/8 | 3/12 | 4/16 | 5/20 | 0.25 |
| 3/4 | 6/8 | 9/12 | 12/16 | 15/20 | 0.75 |
| 1/5 | 2/10 | 3/15 | 4/20 | 5/25 | 0.2 |
| 2/5 | 4/10 | 6/15 | 8/20 | 10/25 | 0.4 |
| 1/8 | 2/16 | 3/24 | 4/32 | 5/40 | 0.125 |
Kids shouldn’t memorize this chart. They should be able to rebuild any row with multiplication facts. The chart is for checking work.
How to tell if two fractions are equivalent
Cross multiply
Multiply each numerator by the other fraction’s denominator. If the products match, the fractions are equivalent.
Are 4/6 and 6/9 equivalent?
4 × 9 = 36
6 × 6 = 36
Same product, so yes.
Are 3/4 and 5/7 equivalent?
3 × 7 = 21
4 × 5 = 20
Different, so no. (3/4 is slightly bigger.)
Simplify both
Reduce each fraction to simplest form and compare. 10/15 simplifies to 2/3 and 14/21 simplifies to 2/3, so they’re equivalent. This way takes longer but helps kids see why the answer is yes.
Where kids actually use equivalent fractions
Comparing fractions. Which is bigger, 3/4 or 5/8? Rewrite 3/4 as 6/8. Now it’s easy: 6/8 > 5/8.
Adding and subtracting. You can’t add 1/3 + 1/4 until the pieces are the same size. Use twelfths: 1/3 = 4/12 and 1/4 = 3/12, so the sum is 7/12.
Decimals and percents. 3/5 = 60/100, which is 0.6 or 60%. Getting a denominator of 10 or 100 turns a fraction into a decimal instantly.
Kitchen math. A recipe needs 3/4 cup, but the only clean scoop is 1/8 cup. Since 3/4 = 6/8, that’s 6 scoops.
Common mistakes with equivalent fractions
- Adding instead of multiplying. Turning 1/2 into 2/3 by adding 1 to the top and bottom. The value changes.
- Changing only one part. Doubling the denominator of 3/4 to get 3/8 cuts the amount in half.
- Thinking bigger numbers mean a bigger fraction. 50/100 isn’t more than 1/2. It’s the same.
- Stopping too early when simplifying. 12/18 ÷ 2/2 = 6/9, but 6/9 still simplifies to 2/3.
- Dividing by a number that doesn’t fit both. You can’t divide 9/12 by 2/2, because 9 ÷ 2 isn’t a whole number.
Practice problems
- Write two fractions equivalent to 1/3.
- Fill in the blank: 3/4 = ?/20
- Fill in the blank: 2/5 = 8/?
- Simplify 15/25.
- Simplify 36/48.
- Are 6/10 and 9/15 equivalent?
- Are 5/6 and 7/9 equivalent?
- A recipe calls for 2/3 cup of oats, and you only have a 1/6 cup scoop. How many scoops do you need?
Answers
- Any fraction where the bottom is 3 times the top works, such as 2/6, 3/9 or 4/12.
- 15. The denominator went 4 × 5 = 20, so the top is 3 × 5 = 15.
- 20. The numerator went 2 × 4 = 8, so the bottom is 5 × 4 = 20.
- 3/5. Divide both by 5.
- 3/4. The greatest common factor is 12: 36 ÷ 12 = 3 and 48 ÷ 12 = 4.
- Yes. 6 × 15 = 90 and 10 × 9 = 90. Both simplify to 3/5.
- No. 5 × 9 = 45 but 6 × 7 = 42.
- 4 scoops, because 2/3 = 4/6.
If your kid is stuck on equivalent fractions
Equivalent fractions sit on top of two older skills. The first is knowing what a fraction means: that the bottom number tells how many equal pieces the whole is cut into, and the top tells how many you have. A kid who treats 3/4 as two unrelated numbers will never see why 6/8 is the same. The second is fast multiplication and division facts. If finding 3 × 4 or the factors of 24 takes real effort, every equivalent fraction problem becomes a slog.
Most kids meet equivalent fractions in third and fourth grade, and our post on math skills by grade level shows where they fit. This topic matters more than it looks. Adding fractions, ratios, percents and a lot of algebra all lean on it, which is why we argue that algebra trouble usually starts with fourth grade fractions. Short daily practice closes these gaps faster than cramming, as we explain in why 20 minutes a day works.
Frequently asked questions
What are equivalent fractions?
Equivalent fractions are fractions with different numerators and denominators that equal the same amount, such as 2/3, 4/6 and 8/12.
How do you find equivalent fractions?
Multiply or divide the numerator and denominator by the same nonzero number. Multiplying 2/7 by 3/3 gives 6/21, which is equivalent.
What is a fractional equivalent?
It usually means the fraction that equals a given decimal or percent. The fractional equivalent of 0.75 is 3/4, and of 20% is 1/5. People also use it to mean an equivalent fraction.
Is 2/4 equivalent to 1/2?
Yes. Divide the top and bottom of 2/4 by 2 and you get 1/2. Cross multiplying confirms it: 2 × 2 = 4 and 4 × 1 = 4.
What grade learns equivalent fractions?
In most US schools, third graders start with simple equivalent fractions using pictures and number lines, and fourth graders learn the multiply and divide rule and use it to compare fractions.
How many equivalent fractions does a fraction have?
Infinitely many. You can multiply the top and bottom by 2, 3, 4, 1,000 or any other whole number, and each one gives a new equivalent fraction.
Find the actual gap
When fractions won’t click, the missing piece is often a year or two back. Math Anon begins with a short adaptive assessment that checks the skills underneath equivalent fractions, like multiplication facts, factors and what a fraction represents, and hands you a written report of exactly what’s missing.
Then your kid practices those specific skills for about 20 minutes a day, and you get a progress report each week. The assessment costs $49, fully credited back on your first month. Start the assessment or check pricing.
