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Dividing fractions might seem tricky at first, but it’s straightforward once you understand the process. Here’s how you do it:
Steps to Divide Fractions
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Keep the first fraction as it is:
- Don’t change the first fraction; just leave it as it is.
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Change the division sign to multiplication:
- Instead of dividing by a fraction, you multiply by its reciprocal.
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Flip the second fraction (find its reciprocal):
- The reciprocal of a fraction is simply swapping its numerator (top number) and denominator (bottom number).
- For example, the reciprocal of <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{2}{3}</annotation></semantics></math>32 is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3}{2}</annotation></semantics></math>23.
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Multiply the fractions:
- Multiply the numerators (top numbers) together to get the new numerator.
- Multiply the denominators (bottom numbers) together to get the new denominator.
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Simplify the result (if necessary):
- If the resulting fraction can be simplified, divide both the numerator and the denominator by their greatest common factor (GCF) to simplify the fraction.
Example
Let’s divide <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3}{4}</annotation></semantics></math>43 by <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>2</mn><mn>5</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{2}{5}</annotation></semantics></math>52:
- Keep the first fraction: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3}{4}</annotation></semantics></math>43
- Change the division sign to multiplication: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3}{4}</annotation></semantics></math>43 × <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{5}{2}</annotation></semantics></math>25
- Flip the second fraction: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3}{4}</annotation></semantics></math>43 × <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{5}{2}</annotation></semantics></math>25
- Multiply the fractions:
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mfrac><mrow><mn>3</mn><mo>×</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>×</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>15</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3 \times 5}{4 \times 2} = \frac{15}{8}</annotation></semantics></math>4×23×5=815 - Simplify the result (if possible):
- <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>15</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{15}{8}</annotation></semantics></math>815 is already in its simplest form, so the answer is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>15</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{15}{8}</annotation></semantics></math>815 or 1<math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>7</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{7}{8}</annotation></semantics></math>87 as a mixed number.
Summary
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction and simplify the result if needed.
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