Find each product or quotient where possible. 76−23\frac{\frac76}{-\frac23}

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 78

1장, 문제 78

Find each product or quotient where possible. $\frac{\frac{7}{6}}{- \frac{2}{3}}$

검증된 단계별 안내

Identify the problem as a division of two fractions: $\frac{7}{6} \div \left(-\frac{2}{3}\right)$.

Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, rewrite the expression as $\frac{7}{6} \times \left(-\frac{3}{2}\right)$.

Multiply the numerators together and the denominators together: numerator = $7 \times (-3)$, denominator = $6 \times 2$.

Write the product as a single fraction: $\frac{7 \times (-3)}{6 \times 2}$.

Simplify the fraction by reducing common factors and handling the negative sign appropriately.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Dividing Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, dividing by 2/3 is the same as multiplying by 3/2.

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together. Simplify the resulting fraction if possible by dividing numerator and denominator by their greatest common divisor.

Simplifying Negative Fractions

A negative fraction can be written with the negative sign in the numerator, denominator, or in front of the fraction. When multiplying or dividing, keep track of the signs: a negative times a positive is negative, and a negative divided by a positive is negative.

Find each product or quotient where possible. 76−23\(\frac{\frac76}{-\frac23}\)