Multiply or divide as indicated. Write answers in lowest terms as needed. $2 and one half divided by 1 and five sevenths$

검증된 단계별 안내

First, convert the mixed numbers to improper fractions. For 2(1/2), multiply the whole number 2 by the denominator 2 and add the numerator 1: $2 \times 2 + 1 = 5$, so $2(1/2) = \frac{5}{2}$. For 1(5/7), multiply the whole number 1 by the denominator 7 and add the numerator 5: $1 \times 7 + 5 = 12$, so $1(5/7) = \frac{12}{7}$.

Rewrite the original expression using the improper fractions: $\frac{5}{2} \div \frac{12}{7}$.

Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, rewrite the division as multiplication by flipping the second fraction: $\frac{5}{2} \times \frac{7}{12}$.

Multiply the numerators together and the denominators together: numerator $5 \times 7 = 35$, denominator $2 \times 12 = 24$, so the product is $\frac{35}{24}$.

Simplify the fraction $\frac{35}{24}$ if possible by finding the greatest common divisor (GCD) of 35 and 24 and dividing numerator and denominator by it. If no common factors other than 1 exist, the fraction is already in lowest terms.

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주요 개념

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Mixed Numbers and Improper Fractions

Mixed numbers combine a whole number and a fraction, such as 2(1/2). To perform operations, convert mixed numbers to improper fractions by multiplying the whole number by the denominator and adding the numerator. This simplifies calculations like multiplication and division.

Division of Fractions

Dividing fractions involves multiplying by the reciprocal of the divisor. For example, to divide by 1(5/7), first convert it to an improper fraction, then flip it and multiply. This method transforms division problems into multiplication ones, making them easier to solve.

Simplifying Fractions

After performing multiplication or division, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD). Simplifying ensures the answer is in lowest terms, making it clearer and easier to interpret.

Multiply or divide as indicated. Write answers in lowest terms as needed. 212÷1572\(\frac{1}{2}\) \(\div\) 1\(\frac{5}{7}\)