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Activity Discussion Math Fractions Reply To: Fractions

• ### Mawar Tanjung

Member
August 17, 2024 at 3:19 pm
0

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

1. Keep the first fraction as it is:

• Don’t change the first fraction; just leave it as it is.
2. Change the division sign to multiplication:

• Instead of dividing by a fraction, you multiply by its reciprocal.
3. 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>[/itex]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>[/itex]23​.
4. 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.
5. 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>[/itex]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>[/itex]52​:

1. 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>[/itex]43​
2. 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>[/itex]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>[/itex]25​
3. 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>[/itex]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>[/itex]25​
4. 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>[/itex]4×23×5​=815​
5. 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>[/itex]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>[/itex]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>[/itex]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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