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Mawar Tanjung

To compare <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">2 \frac{3}{4}</annotation></semantics></math>243​ and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">1 \frac{1}{2}</annotation></semantics></math>121​, first convert the mixed numbers to improper fractions:

  1. Convert <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">2 \frac{3}{4}</annotation></semantics></math>243​:

    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>2</mn><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>=</mo><mn>2</mn><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>8</mn><mn>4</mn></mfrac><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>11</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}</annotation></semantics></math>243​=2+43​=48​+43​=411​

  2. Convert <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">1 \frac{1}{2}</annotation></semantics></math>121​:

    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>1</mn><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mn>2</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}</annotation></semantics></math>121​=1+21​=22​+21​=23​

Now, compare the two improper fractions:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>11</mn><mn>4</mn></mfrac><mtext> and </mtext><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{11}{4} \text{ and } \frac{3}{2}</annotation></semantics></math>411​ and 23​

To compare them, convert <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​ to a fraction with the same denominator as <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>11</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{11}{4}</annotation></semantics></math>411​:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>×</mo><mn>2</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>6</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4}</annotation></semantics></math>23​=2×23×2​=46​

Now compare <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>11</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{11}{4}</annotation></semantics></math>411​ and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>6</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{6}{4}</annotation></semantics></math>46​:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>11</mn><mn>4</mn></mfrac><mo>></mo><mfrac><mn>6</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{11}{4} > \frac{6}{4}</annotation></semantics></math>411​>46​

Therefore, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">2 \frac{3}{4}</annotation></semantics></math>243​ is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">1 \frac{1}{2}</annotation></semantics></math>121​.

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