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Evaluate. (5)/(2)÷(5)/(7)=

Evaluate.\newline52÷57= \frac{5}{2} \div \frac{5}{7}=

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Add, subtract, multiply, and divide integersright chevron icon

Full solution

Q. Evaluate.\newline52÷57= \frac{5}{2} \div \frac{5}{7}=
  1. Understand Operation: Understand the operation to be performed.\newlineWe need to divide the fraction (5/2)(5/2) by the fraction (5/7)(5/7). In mathematical terms, this is written as (5/2)÷(5/7)(5/2) \div (5/7).
  2. Convert to Multiplication: Convert the division of fractions into multiplication.\newlineTo divide by a fraction, we multiply by its reciprocal. The reciprocal of (57)(\frac{5}{7}) is (75)(\frac{7}{5}).\newline(52)÷(57)=(52)×(75)(\frac{5}{2}) \div (\frac{5}{7}) = (\frac{5}{2}) \times (\frac{7}{5})
  3. Multiply Numerators and Denominators: Multiply the numerators and denominators.\newlineNow we multiply the numerators together and the denominators together.\newlineNumerator: 5×7=355 \times 7 = 35\newlineDenominator: 2×5=102 \times 5 = 10\newlineSo, (52)×(75)=3510(\frac{5}{2}) \times (\frac{7}{5}) = \frac{35}{10}
  4. Simplify Fraction: Simplify the fraction, if possible.\newlineThe fraction 3510\frac{35}{10} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 55.\newline35÷5=735 \div 5 = 7\newline10÷5=210 \div 5 = 2\newlineSo, 3510\frac{35}{10} simplifies to 72\frac{7}{2}.

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