Adding and subtracting fractions
You can only add or subtract fractions that have the same denominator. If the denominators differ, multiply the top and bottom of each fraction so that they match: this is finding a common denominator.
Example: 1/2 + 1/3
- Use the common denominator 6: 1/2 = 3/6 and 1/3 = 2/6.
- Add the numerators: 3/6 + 2/6 = 5/6.
Subtracting works the same way: 3/4 − 1/6 = 9/12 − 2/12 = 7/12.
A shortcut that always works: (a/b) + (c/d) = (a·d + c·b) / (b·d), then simplify. That is exactly what the calculator does.
Multiplying fractions
Multiplying is the easiest: numerator times numerator and denominator times denominator. No common denominator is needed.
Example: 2/3 × 3/4 = 6/12 = 1/2.
To take a fraction of a whole number, such as 3/4 of 20, write the number as a fraction: 20/1. Then 3/4 × 20/1 = 60/4 = 15.
Dividing fractions
Dividing by a fraction is the same as multiplying by its reciprocal: flip the second fraction. Teachers often call it "keep, change, flip".
Example: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. So six eighths fit into three quarters.
You cannot divide by zero: a fraction with numerator 0 has no reciprocal.
Simplifying
Simplify a fraction by dividing the numerator and denominator by their greatest common factor (GCF). 6/12 has GCF 6, so 6/12 = 1/2. 18/24 has GCF 6, so 18/24 = 3/4. The calculator always reduces the answer to lowest terms.
Mixed numbers
When the numerator is larger than the denominator, the fraction is improper. You can write it as a mixed number: a whole number plus a fraction. 7/4 + 5/6 = 21/12 + 10/12 = 31/12, which is 2 7/12, because 2 × 12 = 24 and 31 − 24 = 7.
To calculate with a mixed number yourself, first turn it into an improper fraction: 2 1/2 = 5/2.
Fraction to decimal and percent
A fraction is simply a division: 5/6 = 5 ÷ 6 ≈ 0.8333, or 83.33%. Some fractions give a terminating decimal (1/4 = 0.25), others a repeating one (1/3 = 0.333…). For more percentage questions use the percentage calculator, and for longer expressions with brackets the scientific calculator.
Fractions in everyday life
You meet fractions in recipes (¾ cup), in sales (buy two, get the third free), when sharing pizza and in DIY, where inches are measured in eighths and sixteenths. Music (three-four time) and probability use fractions too.
Common mistakes
- Adding numerators and denominators straight across: 1/2 + 1/3 is not 2/5. Find a common denominator first.
- Forgetting to simplify: 4/8 is correct, but 1/2 is the tidy answer, and tests usually ask for lowest terms.
- Flipping the wrong fraction when dividing: always flip the second fraction, the divisor, never the first.
- Losing a minus sign: −1/2 + 1/3 = −3/6 + 2/6 = −1/6. Watch the sign at every step.
Use the calculator to check your answers while you practise, so you can see where a mistake crept in.
Frequently asked questions
How do I add fractions with different denominators?
Find a common denominator, adjust the numerators, then add the numerators. Finally, simplify the result.
How do I multiply fractions?
Multiply the numerators together and the denominators together. 2/5 × 3/4 = 6/20 = 3/10.
How do I divide by a fraction?
Multiply by the reciprocal of the second fraction. 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor. 12/16 becomes 3/4 (both divided by 4).
What is a mixed number?
A whole number with a fraction, such as 2 1/2. It is another way of writing an improper fraction, in this case 5/2.
Can I use negative fractions?
Yes. Put the minus sign on the numerator, for example −1/2.
Last reviewed: 2026-10-06. Results are estimates for information only.