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Pre-Algebra

Operations with Fractions

Lesson

A fraction like 34\frac{3}{4} has a numerator on top and a denominator on the bottom. There are four operations to know.

Adding and subtracting

Get a common denominator first, then add or subtract just the numerators.

13+16=26+16=36=12\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}

Multiplying

Multiply numerators across the top, denominators across the bottom. No common denominator needed.

23×34=2⋅33⋅4=612=12\frac{2}{3} \times \frac{3}{4} = \frac{2 \cdot 3}{3 \cdot 4} = \frac{6}{12} = \frac{1}{2}

Dividing

Flip (reciprocal) the second fraction, then multiply.

12÷14=12×41=42=2\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2

Always simplify your final answer to lowest terms.

How to type your answer

Use a / for fractions and write them in lowest terms. If the answer is a whole number, just write the number. If it’s an improper fraction (numerator larger than denominator), leave it improper — don’t mix-number it. Examples: 3/4, 5/6, 7/4, 2, -1/3.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

14+24\frac{1}{4} + \frac{2}{4}

Problem 2

58−18\frac{5}{8} - \frac{1}{8}

Problem 3

12×13\frac{1}{2} \times \frac{1}{3}

Problem 4

25+15\frac{2}{5} + \frac{1}{5}

Practice

Standard problems matching the lesson.

Problem 5

13+16\frac{1}{3} + \frac{1}{6}

Problem 6

34−12\frac{3}{4} - \frac{1}{2}

Problem 7

23+14\frac{2}{3} + \frac{1}{4}

Problem 8

56−13\frac{5}{6} - \frac{1}{3}

Problem 9

23×34\frac{2}{3} \times \frac{3}{4}

Problem 10

35×29\frac{3}{5} \times \frac{2}{9}

Problem 11

12÷14\frac{1}{2} \div \frac{1}{4}

Problem 12

34÷12\frac{3}{4} \div \frac{1}{2}

Problem 13

25÷415\frac{2}{5} \div \frac{4}{15}

Problem 14

16+34\frac{1}{6} + \frac{3}{4}

Problem 15

78−14\frac{7}{8} - \frac{1}{4}

Problem 16

45×58\frac{4}{5} \times \frac{5}{8}

Problem 17

23−14\frac{2}{3} - \frac{1}{4}

Problem 18

34+58\frac{3}{4} + \frac{5}{8}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

14−23\frac{1}{4} - \frac{2}{3}

Problem 20

56+78\frac{5}{6} + \frac{7}{8}

Problem 21

38÷94\frac{3}{8} \div \frac{9}{4}

Problem 22

23−56+12\frac{2}{3} - \frac{5}{6} + \frac{1}{2}

Problem 23

710×514\frac{7}{10} \times \frac{5}{14}

Problem 24

−34+56-\frac{3}{4} + \frac{5}{6}

Problem 25

1−14−381 - \frac{1}{4} - \frac{3}{8}

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