Question

6. Evalúa la siguiente resta: \( \frac{15}{72}-\frac{13}{74} \). \( \square \)

Ask by Gross Davies. in Mexico
Feb 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

La resta es \( \frac{29}{888} \) o \( 0.03265 \).

Solution

Calculate or simplify the expression \( \frac{15}{72}-\frac{13}{74} \). Calculate the value by following steps: - step0: Calculate: \(\frac{15}{72}-\frac{13}{74}\) - step1: Reduce the fraction: \(\frac{5}{24}-\frac{13}{74}\) - step2: Reduce fractions to a common denominator: \(\frac{5\times 37}{24\times 37}-\frac{13\times 12}{74\times 12}\) - step3: Multiply the numbers: \(\frac{5\times 37}{888}-\frac{13\times 12}{74\times 12}\) - step4: Multiply the numbers: \(\frac{5\times 37}{888}-\frac{13\times 12}{888}\) - step5: Transform the expression: \(\frac{5\times 37-13\times 12}{888}\) - step6: Multiply the numbers: \(\frac{185-13\times 12}{888}\) - step7: Multiply the numbers: \(\frac{185-156}{888}\) - step8: Subtract the numbers: \(\frac{29}{888}\) La resta de \( \frac{15}{72} \) y \( \frac{13}{74} \) es igual a \( \frac{29}{888} \) o aproximadamente \( 0.03265 \).

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The Deep Dive

Para realizar la resta de las fracciones, primero debemos encontrar un denominador común. El mínimo común múltiplo (MCM) de 72 y 74 es 5328. Al reescribir las fracciones con el nuevo denominador, tenemos: \( \frac{15 \cdot 74}{5328} - \frac{13 \cdot 72}{5328} = \frac{1110}{5328} - \frac{936}{5328} = \frac{174}{5328} \). Simplificando, esto da \( \frac{29}{888} \). Por otro lado, es importante recordar que trabajar con fracciones puede ser un poco complicado. Para evitar errores comunes, asegúrate de calcular bien el MCM y de multiplicar correctamente numerador y denominador al cambiar de denominadores. ¡Tomarte tu tiempo y revisar tus cálculos puede ser la clave para evitar errores!

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