What is a fraction?
A fraction represents part of a whole. It has a numerator (the top number — how many parts you have) and a denominator (the bottom number — how many equal parts make up the whole). In 3/8, the numerator is 3 and the denominator is 8: imagine a pie cut into 8 slices, of which you have 3. The denominator can never be 0, because dividing a whole into zero parts is undefined.
Adding fractions
You can only add fractions that share a denominator. Find a common denominator (the quickest reliable choice is the product of the two denominators, or the least common multiple), rewrite each fraction, then add the numerators and simplify. Example: 3/4 + 1/6. The least common multiple of 4 and 6 is 12, so 3/4 becomes 9/12 and 1/6 becomes 2/12, giving 9/12 + 2/12 = 11/12.
Subtracting fractions
Subtraction works exactly like addition — get a common denominator first, then subtract the numerators. For example, 3/4 − 1/6 = 9/12 − 2/12 = 7/12.
Multiplying fractions
No common denominator needed. Multiply the numerators together and the denominators together, then simplify. Example: 3/4 × 1/6 = 3/24 = 1/8.
Dividing fractions
To divide, multiply the first fraction by the reciprocal of the second (swap its numerator and denominator). Example: 3/4 ÷ 1/6 = 3/4 × 6/1 = 18/4 = 9/2.
Simplifying fractions
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. Divide both by their greatest common factor. For example, 220/440 divides by 220 to give the much simpler 1/2.
Converting between fractions and decimals
To turn a decimal into a fraction, use the number of decimal places as a power of 10 for the denominator, then simplify — 0.1234 = 1234/10000 = 617/5000. To turn a fraction into a decimal, divide the numerator by the denominator. Some results terminate (1/8 = 0.125) and some repeat (2/7 = 0.285714…); this calculator marks the repeating block in brackets.
Frequently asked questions
Give both fractions the same denominator, add the numerators, then simplify. For example, 3/4 + 1/6: the common denominator is 12, so 9/12 + 2/12 = 11/12.
Multiply the numerators together and the denominators together, then simplify. You do not need a common denominator. For example, 3/4 × 1/6 = 3/24 = 1/8.
Multiply the first fraction by the reciprocal (flip) of the second, then simplify. For example, 3/4 ÷ 1/6 = 3/4 × 6/1 = 18/4 = 9/2.
Divide the numerator and denominator by their greatest common factor (GCF). For example, 21/98 shares a factor of 7, so it simplifies to 3/14.
Use the number of decimal places as a power of 10 for the denominator, then simplify. 1.375 has three decimal places, so it is 1375/1000 = 11/8 = 1 3/8.
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