• Math

  Fraction

  Posted by Delly Kuku on September 25, 2024 at 4:39 pm

  Can you multiply 3 3/4 by 2 1/2?

  Mawar Tanjung replied 1 week, 5 days ago 2 Members · 1 Reply

  • @fraction
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  Mawar Tanjung

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  September 27, 2024 at 12:58 pm

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  1. Convert <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>3 \frac{3}{4}</annotation></semantics></math>343​:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>×</mo><mn>4</mn><mo>+</mo><mn>3</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>12</mn><mo>+</mo><mn>3</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>15</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}</annotation></semantics></math>343​=43×4+3​=412+3​=415​

  2. Convert <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>2 \frac{1}{2}</annotation></semantics></math>221​:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>2</mn><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}</annotation></semantics></math>221​=22×2+1​=24+1​=25​

  Now, we multiply the two improper fractions:

  <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mfrac><mn>15</mn><mn>4</mn></mfrac><mo>×</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>15</mn><mo>×</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>×</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>75</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{15}{4} \times \frac{5}{2} = \frac{15 \times 5}{4 \times 2} = \frac{75}{8}</annotation></semantics></math>415​×25​=4×215×5​=875​

  To convert <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>75</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{75}{8}</annotation></semantics></math>875​ back to a mixed number:

  1. Divide 75 by 8, which gives 9 with a remainder of 3.
  2. So, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>75</mn><mn>8</mn></mfrac><mo>=</mo><mn>9</mn><mfrac><mn>3</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{75}{8} = 9 \frac{3}{8}</annotation></semantics></math>875​=983​.

  Thus, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>×</mo><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mn>9</mn><mfrac><mn>3</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>3 \frac{3}{4} \times 2 \frac{1}{2} = 9 \frac{3}{8}</annotation></semantics></math>343​×221​=983​.

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