Fraction Calculator
Add, subtract, multiply and divide fractions — with full step-by-step working shown.
Step by step calculations
Enter fractions in the calculator to see the step by step calculations.
Fraction Calculator Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
Fractions are everywhere once you look
You're doubling a recipe that calls for ¾ of a cup of flour. How much do you need? 2 × ¾ = 1½ cups. Or a drill bit labelled ⅜ inch — how wide is that in decimal? 0.375 inches. Or three friends split a pizza: you ate ⅓, she had ¼, they had the rest. What fraction was left? These aren't contrived maths problems — they're Tuesday.
Worked example
"A recipe uses ⅔ cup of sugar. You want to make 1½ times the recipe. How much sugar do you need?"
Convert 1½ to fraction: 3/2
Multiply: 2/3 × 3/2
= (2 × 3) / (3 × 2)
= 6/6
Result: 1 full cup of sugar
Multiplying fractions: numerator × numerator, denominator × denominator. Then simplify.
Adding fractions — the key rule
- → Same denominator: 1/4 + 2/4 = 3/4. Just add the tops. "I spent ¼ of my budget on food and 2/4 on rent — that's ¾ gone."
- → Different denominators: find the LCM first. 1/3 + 1/4 → LCM is 12 → 4/12 + 3/12 = 7/12. "I walked ⅓ of the journey, then ¼ more."
- → Time as fractions: ¾ of an hour = 45 minutes. ⅙ of an hour = 10 minutes. Bus timetables and cooking timers work in fraction-of-an-hour logic constantly.
Dividing fractions — Keep, Flip, Change
To divide by a fraction, multiply by its reciprocal. 3/4 ÷ 1/2 → Keep 3/4, Flip 1/2 to 2/1, Change ÷ to × → 3/4 × 2/1 = 6/4 = 3/2 = 1½. Useful when splitting an amount equally: "divide ¾ of a cake among 3 people" = ¾ ÷ 3 = ¼ each.
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Fraction Calculator
Fractions are a way to represent parts of a whole. They are used in everyday life for things like cooking (half a cup of flour), measuring (a quarter of a metre), sharing items (three-quarters of a pizza), and understanding proportions. Being comfortable with fractions helps you make sense of quantities and measurements in many situations.
The key to working with fractions is understanding that you can only directly combine or compare them when they refer to the same 'size' of parts. This means they need to have a common denominator, which is the bottom number of the fraction. Once the parts are the same size, you can easily add, subtract, multiply, or divide them.
Four types explained
Add fractions
To add fractions, first find the lowest common multiple (LCM) of their denominators. Convert each fraction into an equivalent fraction using this common denominator. Then, add the numerators together and keep the common denominator. Finally, simplify the resulting fraction if possible.
Let's add 1/3 and 1/4. The denominators are 3 and 4. The lowest common multiple of 3 and 4 is 12. To convert 1/3, we multiply the numerator and denominator by 4, giving 4/12. To convert 1/4, we multiply the numerator and denominator by 3, giving 3/12. Now we add the new numerators: 4 + 3 = 7. The denominator stays 12. So, 1/3 + 1/4 = 7/12. This fraction cannot be simplified further.
Subtract fractions
To subtract fractions, first find the lowest common multiple (LCM) of their denominators. Convert each fraction into an equivalent fraction using this common denominator. Then, subtract the second numerator from the first numerator and keep the common denominator. Finally, simplify the resulting fraction if possible.
Let's subtract 1/6 from 3/4. The denominators are 4 and 6. The lowest common multiple of 4 and 6 is 12. To convert 3/4, we multiply the numerator and denominator by 3, giving 9/12. To convert 1/6, we multiply the numerator and denominator by 2, giving 2/12. Now we subtract the new numerators: 9 - 2 = 7. The denominator stays 12. So, 3/4 - 1/6 = 7/12. This fraction cannot be simplified further.
Multiply fractions
To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Simplify the resulting fraction if possible.
Let's multiply 2/3 by 3/4. First, multiply the numerators: 2 × 3 = 6. Then, multiply the denominators: 3 × 4 = 12. This gives us the fraction 6/12. To simplify, we find the greatest common divisor of 6 and 12, which is 6. Divide both the numerator and denominator by 6: 6 ÷ 6 = 1 and 12 ÷ 6 = 2. So, 2/3 × 3/4 = 1/2.
Divide fractions
To divide fractions, you 'flip' the second fraction (find its reciprocal) and then multiply it by the first fraction. Simplify the resulting fraction if possible.
Let's divide 3/4 by 1/2. First, 'flip' the second fraction, 1/2, to get its reciprocal, which is 2/1. Now, multiply the first fraction (3/4) by this reciprocal (2/1): 3/4 × 2/1. Multiply the numerators: 3 × 2 = 6. Multiply the denominators: 4 × 1 = 4. This gives us 6/4. To simplify, the greatest common divisor of 6 and 4 is 2. Divide both by 2: 6 ÷ 2 = 3 and 4 ÷ 2 = 2. So, 3/4 ÷ 1/2 = 3/2, which can also be written as the mixed number 1 1/2.
Common mistakes to avoid
- 1/2 + 1/3 = 2/5:This mistake happens when students add the numerators together and the denominators together. You can only add or subtract fractions if they have the same denominator. To add 1/2 and 1/3, find a common denominator (6). 1/2 becomes 3/6, and 1/3 becomes 2/6. Then, add the numerators: 3/6 + 2/6 = 5/6.
- 3/4 - 1/2 = 2/2 = 1:This error occurs when students subtract numerators without first finding a common denominator. The parts must be of the same size before you can subtract them. To subtract 1/2 from 3/4, find a common denominator (4). 1/2 becomes 2/4. Then, subtract the numerators: 3/4 - 2/4 = 1/4.
- 1/2 ÷ 1/3 = 1/6:This mistake is common when students treat division like multiplication, multiplying numerators and denominators directly. Division requires an extra step. To divide 1/2 by 1/3, you must 'flip' the second fraction (1/3 becomes 3/1) and then multiply: 1/2 × 3/1 = 3/2.
- 2/4 + 1/4 = 3/8:This happens when students correctly add the numerators but then also add the denominators. When fractions have a common denominator, it stays the same. When adding fractions with the same denominator, you only add the numerators. So, 2/4 + 1/4 = 3/4.