Evaluate. (5)/(2)÷(5)/(7)=

Understand Operation: Understand the operation to be performed. We need to divide the fraction (5/2) by the fraction (5/7). In mathematical terms, this is written as (5/2) ÷ (5/7).Convert to Multiplication: Convert the division of fractions into multiplication. To divide by a fraction, we multiply by its reciprocal. The reciprocal of (5/7) is (7/5). (5/2) ÷ (5/7) = (5/2) × (7/5)Multiply Numerators and Denominators: Multiply the numerators and denominators. Now we multiply the numerators together and the denominators together. Numerator: 5 × 7 = 35 Denominator: 2 × 5 = 10 So, (5/2) × (7/5) = 35/10Simplify Fraction: Simplify the fraction, if possible. The fraction 35/10 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5. 35 ÷ 5 = 7 10 ÷ 5 = 2 So, 35/10 simplifies to 7/2.

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Math Problems

Grade 7

Add, subtract, multiply, and divide integers

Full solution

Q. Evaluate.

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\frac{5}{2} \div \frac{5}{7}=

Understand Operation: Understand the operation to be performed. $\newline$ We need to divide the fraction $(5/2)$ by the fraction $(5/7)$ . In mathematical terms, this is written as $(5/2) \div (5/7)$ .
Convert to Multiplication: Convert the division of fractions into multiplication. $\newline$ To divide by a fraction, we multiply by its reciprocal. The reciprocal of $(\frac{5}{7})$ is $(\frac{7}{5})$ . $\newline$ $(\frac{5}{2}) \div (\frac{5}{7}) = (\frac{5}{2}) \times (\frac{7}{5})$
Multiply Numerators and Denominators: Multiply the numerators and denominators. $\newline$ Now we multiply the numerators together and the denominators together. $\newline$ Numerator: $5 \times 7 = 35$ $\newline$ Denominator: $2 \times 5 = 10$ $\newline$ So, $(\frac{5}{2}) \times (\frac{7}{5}) = \frac{35}{10}$
Simplify Fraction: Simplify the fraction, if possible. $\newline$ The fraction $\frac{35}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $5$ . $\newline$ $35 \div 5 = 7$ $\newline$ $10 \div 5 = 2$ $\newline$ So, $\frac{35}{10}$ simplifies to $\frac{7}{2}$ .