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  Fraction

  Posted by Yuliana YM on August 3, 2024 at 1:42 pm

  How do you multiply fractions?

  Aakrisha Timalsina replied 8 months, 2 weeks ago 2 Members · 1 Reply
• 1 Reply

• 

  Aakrisha Timalsina

  Member

  August 5, 2024 at 3:59 pm

  Multiplying fractions is a straightforward process. Here’s how you can do it:

  1. Multiply the Numerators

  a. Identify the Numerators: Look at the top numbers of the fractions you are multiplying. For example, in <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​ and <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​, the numerators are 2 and 3.

  b. Multiply the Numerators Together: Multiply these two numerators. Using the example, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mo>×</mo><mn>3</mn><mo>=</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>2 \times 3 = 6</annotation></semantics></math>2×3=6.

  2. Multiply the Denominators

  a. Identify the Denominators: Look at the bottom numbers of the fractions. For <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​ and <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​, the denominators are 5 and 4.

  b. Multiply the Denominators Together: Multiply these two denominators. Using the example, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>5</mn><mo>×</mo><mn>4</mn><mo>=</mo><mn>20</mn></mrow><annotation encoding=”application/x-tex”>5 \times 4 = 20</annotation></semantics></math>5×4=20.

  3. Form the New Fraction

  a. Create the Fraction: Place the product of the numerators over the product of the denominators. For the example, this becomes <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>6</mn><mn>20</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{6}{20}</annotation></semantics></math>206​.

  4. Simplify the Fraction (if needed)

  a. Find the Greatest Common Divisor (GCD): Determine the GCD of the numerator and the denominator. For <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>6</mn><mn>20</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{6}{20}</annotation></semantics></math>206​, the GCD of 6 and 20 is 2.

  b. Divide by the GCD: Simplify the fraction by dividing both the numerator and the denominator by their GCD. Thus, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mrow><mn>6</mn><mo>÷</mo><mn>2</mn></mrow><mrow><mn>20</mn><mo>÷</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>3</mn><mn>10</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{6 \div 2}{20 \div 2} = \frac{3}{10}</annotation></semantics></math>20÷26÷2​=103​.

  Example Calculation:

  Multiply <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>2</mn><mn>5</mn></mfrac><mtext> and </mtext><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{2}{5} \text{ and } \frac{3}{4}</annotation></semantics></math>52​ and 43​:

  1. Multiply the Numerators: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mo>×</mo><mn>3</mn><mo>=</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>2 \times 3 = 6</annotation></semantics></math>2×3=6
  2. Multiply the Denominators: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>5</mn><mo>×</mo><mn>4</mn><mo>=</mo><mn>20</mn></mrow><annotation encoding=”application/x-tex”>5 \times 4 = 20</annotation></semantics></math>5×4=20
  3. Form the New Fraction: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>6</mn><mn>20</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{6}{20}</annotation></semantics></math>206​
  4. Simplify the Fraction: Divide both numerator and denominator by their GCD (2):
     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mfrac><mrow><mn>6</mn><mo>÷</mo><mn>2</mn></mrow><mrow><mn>20</mn><mo>÷</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>3</mn><mn>10</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{6 \div 2}{20 \div 2} = \frac{3}{10}</annotation></semantics></math>20÷26÷2​=103​

  So, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>2</mn><mn>5</mn></mfrac><mo>×</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>3</mn><mn>10</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{2}{5} \times \frac{3}{4} = \frac{3}{10}</annotation></semantics></math>52​×43​=103​.

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