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Fraction Operations Visualizer

Add, subtract, multiply, or divide any two fractions (including mixed numbers). See the answer with fraction bar models for addition and subtraction, an area model for multiplication, and step-by-step solutions with automatic simplification.

First fraction

+

Second fraction

The whole number field is optional. Leave it empty for proper fractions.

Try an example

Answer

712\frac{7}{12}

Fraction Bar Model

1/31/4convert to 12ths4/123/127/12

Step-by-Step Solution

1
13+14\frac{1}{3} + \frac{1}{4}
2
LCD(3,4)=12\text{LCD}(3, 4) = 12
3
1×43×4+1×34×3=412+312\frac{1 \times 4}{3 \times 4} + \frac{1 \times 3}{4 \times 3} = \frac{4}{12} + \frac{3}{12}
4
4+312=712\frac{4 + 3}{12} = \frac{7}{12}
5
=712= \frac{7}{12}

Reference Guide

Adding and Subtracting Fractions

To add or subtract fractions, they must have the same denominator (bottom number). If they do not, find the Least Common Denominator (LCD) and convert both fractions.

13+14=412+312=712\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}

Once the denominators match, add or subtract the numerators (top numbers) and keep the denominator the same. Then simplify if possible.

Multiplying Fractions

Multiplying fractions is simpler: multiply the numerators together and multiply the denominators together. No common denominator needed.

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

The area model shows this visually: shade rows for the first fraction and columns for the second. The overlap is the product.

Dividing Fractions

To divide fractions, use the "Keep, Change, Flip" method. Keep the first fraction, change the division sign to multiplication, and flip (take the reciprocal of) the second fraction.

34÷12=34×21=64=32\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2}

Then multiply as usual. Dividing by a fraction is the same as multiplying by its reciprocal.

Working with Mixed Numbers

A mixed number like 2132\frac{1}{3} combines a whole number and a fraction. Before doing any operation, convert it to an improper fraction first.

213=2×3+13=732\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}

After computing your answer, you can convert back to a mixed number by dividing the numerator by the denominator.