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Fractions Help

Add, subtract, multiply, divide and simplify fractions step by step, with worked examples.

Fractions follow a few simple rules. To add or subtract, make the bottoms (denominators) the same. To multiply, multiply straight across. To divide, flip the second fraction and multiply. Always simplify at the end.

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Example problems & solutions

Q

Add 3/4 + 1/6

A
  1. Find a common denominator: the least common multiple of 4 and 6 is 12.
  2. Rewrite each fraction: 3/4 = 9/12 and 1/6 = 2/12.
  3. Add the numerators: 9/12 + 2/12 = 11/12.
  4. 11 and 12 share no common factor, so 11/12 is already simplified.

Answer: 3/4 + 1/6 = 11/12

Q

Subtract 5/6 − 1/4

A
  1. The least common multiple of 6 and 4 is 12.
  2. Rewrite: 5/6 = 10/12 and 1/4 = 3/12.
  3. Subtract the numerators: 10/12 − 3/12 = 7/12.

Answer: 5/6 − 1/4 = 7/12

Q

Multiply 2/3 × 9/10

A
  1. Multiply the numerators: 2 × 9 = 18.
  2. Multiply the denominators: 3 × 10 = 30.
  3. Simplify 18/30 by dividing top and bottom by 6: 3/5.

Answer: 2/3 × 9/10 = 3/5

Q

Divide 3/5 ÷ 9/10

A
  1. Keep the first fraction, change ÷ to ×, and flip the second: 3/5 × 10/9.
  2. Multiply: (3 × 10)/(5 × 9) = 30/45.
  3. Simplify by dividing top and bottom by 15: 2/3.

Answer: 3/5 ÷ 9/10 = 2/3

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Frequently asked questions

How do you add fractions with different denominators?

Find the least common multiple of the denominators, rewrite each fraction with that denominator, then add the numerators and keep the denominator. Simplify if you can.

How do you divide fractions?

Keep the first fraction, change division to multiplication, and flip the second fraction (use its reciprocal). Then multiply across and simplify.

How do you simplify a fraction?

Divide the numerator and denominator by their greatest common factor. For example, 18/30 has a greatest common factor of 6, so it simplifies to 3/5.

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