StringMash.com

Fraction calculator

Add, subtract, multiply and divide fractions, with the steps and bars to see them.

9 characters
Updates as you type

The working and bars are below

Show the steps
1/41/6= 5/12
  1. The bottoms are different, so find a number both 4 and 6 go into. The smallest is 12.
  2. 1/4 = 3/12, multiplying top and bottom by 3.
  3. 1/6 = 2/12, multiplying top and bottom by 2.
  4. Now add the tops: 3 + 2 = 5. That's 5/12.

Put this converter on your site

Paste this into your page's HTML. The converter keeps the pair and settings it has now, and it runs in your reader's browser like it does here.

The credit line under the frame is optional. We'd be grateful if you kept it. How embedding works

Using the calculator

Type fractions with + − × or ÷ between them, like 1/4 + 1/6. You can chain as many as you like, as in 1/2 + 1/3 + 1/4. × and ÷ are done before + and −, as usual, and the steps take each part in turn. Mixed numbers go in with a space, as in 2 3/4, and a whole number on its own is fine too. Decimals work. 1.5 becomes 3/2, exactly. The answer is always simplified. On a keyboard without × or ÷, x and the words divided by work instead; a / always means a fraction.

Show the steps explains the working line by line, with fraction bars underneath: one bar for each fraction and one for the answer, all the same length, so you can see how they compare. Answer as switches between a mixed number such as 1 3/4, an improper fraction such as 7/4, and a decimal.

Type a single fraction, like 18/24, to simplify it. Put one sum on each line to do several at once.

Adding and subtracting fractions

Fractions can only be added when they're cut into the same size of piece. A quarter and a sixth are different sizes, so first find a number both bottoms go into. For 4 and 6, the smallest is 12.

Rewrite each fraction in twelfths. 1/4 becomes 3/12, because 4 × 3 is 12 and the top gets multiplied by 3 as well. 1/6 becomes 2/12. Now the pieces match, so add the tops and keep the bottom: 3/12 + 2/12 = 5/12. Subtraction works the same way, taking the tops away instead.

Practice on screen

Type a fraction like 3/4, or a mixed number like 1 3/4.

0 answered

Multiplying and dividing fractions

Multiplying is the easy one. Multiply the tops together and the bottoms together: 2/3 × 3/4 = 6/12, which simplifies to 1/2. There's no need to match the bottoms first.

To divide, turn the second fraction upside down and multiply instead. 1/2 ÷ 1/4 becomes 1/2 × 4/1, which is 4/2, or 2. It makes sense when you ask the question the division is asking: how many quarters fit into a half? Two.

Simplifying and mixed numbers

A fraction is in its simplest form when no number bigger than 1 divides both the top and the bottom. To get there, divide both by the biggest number that goes into each. 18/24 divides by 6 on both, giving 3/4.

When the top is bigger than the bottom, the fraction is more than a whole. 7/4 is seven quarters, and four of them make a whole, so it's 1 whole and 3 quarters left over: 1 3/4. To go back, multiply the whole number by the bottom and add the top: 1 × 4 + 3 = 7, over 4.

Why top and bottom have the names they do

The bottom number is the denominator, from the Latin for a namer. It names the size of the piece: quarters, sixths, twelfths. The top is the numerator, the counter, which counts how many of those pieces there are. So 3/4 reads as three of the pieces called quarters, which is why only fractions with the same name can be added straight away.

In the classroom

Ages 8 and up, about 25 minutes. Fold paper strips into halves, quarters and eighths, and use them to compare and add fractions before checking with the bars drawn above. Seeing that 2/4 and 1/2 are the same length does more than any rule.

Take it further: set problems where the answer simplifies, such as 1/4 + 1/4, and ask students to explain why the calculator gives 1/2. The number line places fractions in order.

Common Core spreads fractions over grades 3 to 6. Adding with like denominators is 4.NF.B.3, unlike denominators 5.NF.A.1, multiplying 5.NF.B.4, and dividing one fraction by another 6.NS.A.1. In England, pupils add fractions with the same denominator from Year 3, and in Year 6 they add different denominators, multiply pairs of fractions and divide fractions by whole numbers.

Questions

How do I type a mixed number?

Leave a space between the whole number and the fraction: 2 3/4 is two and three quarters.

How do I divide fractions here?

Use ÷, or type divided by, as in 3/4 divided by 1/2. A / is always read as the line in a fraction.

Can I use negative fractions?

Yes. Put a minus sign in front, as in -1/2. A bar for a negative answer is marked below 0.

What's the lowest common denominator?

The smallest number that all the bottoms go into. It keeps the numbers small when adding, though any shared bottom gives the same answer once it's simplified.

Sources

Written, edited and reviewed by .

Added . Last updated and reviewed . What's new