Fraction Calculator with Steps

They show what to multiply the numerator and the denominator by so that the fraction gets the common denominator. First you find the least common denominator — the least common multiple of the denominators — and then divide it by each denominator. For 1/6 + 3/4 the common denominator is 12, so the first fraction is multiplied by 12 ÷ 6 = 2 and the second by 12 ÷ 4 = 3, giving 2/12 + 9/12. Many teachers have students write that small number next to each fraction, which is how it appears in the steps.

When the fraction part of the first number is smaller than the fraction part of the second, you can’t subtract the parts directly: 3 1/4 − 1 2/3 becomes 3 3/12 − 1 8/12, and 3/12 − 8/12 doesn’t work. So one whole is turned into twelfths: 3 3/12 = 2 15/12, because 1 = 12/12. Then the whole parts and the fraction parts subtract normally: 2 − 1 and 15/12 − 8/12, so the answer is 1 7/12. If your class converts to improper fractions instead, switch the method — the answer is the same.

The answer is the same, but the numbers stay small. In 9/4 × 2/3 you can divide 9 and 3 by 3 and then 2 and 4 by 2 right away, leaving 3/2 without multiplying anything big. Multiplying first gives 18/12, and then you still have to find the GCF of 18 and 12. Any numerator can be canceled with any denominator, which is why it is called cross-canceling. The steps show the crossed-out numbers and what is written in their place, just like on paper.

Put the repeating block in parentheses: 0.(3) and 0.1(6). You can also put a bar over the repeating digits, 0.3̅. Dots at the end don’t work, because they don’t show which digits repeat: 0.1666… could be 0.1(6) or the start of something else. On the Decimals tab a repeating decimal turns into a fraction with the algebra shown: x = 0.1(6), 10x = 1.(6), 100x = 16.(6), subtract to get 90x = 15, so x = 1/6.

A fraction in simplest form terminates only when its denominator has no prime factors other than 2 and 5 — only then can it be scaled up to 10, 100 or 1000. The denominator of 3/8 is 8 = 2 × 2 × 2, so 3/8 = 375/1000 = 0.375. The denominator of 1/3 is 3, no power of ten is divisible by 3, and in long division the same remainder keeps coming back, which gives the repeating decimal 0.(3).