Question

learning goal 2.8: students will divide positive fractions. find each quotient. simplify when possible. 4. \\(\frac{3}{8} \div \frac{5}{6}\\) 5. \\(\frac{5}{6} \div \frac{3}{8}\\) 6. \\(\frac{6}{11} \div 9\\) 7. \\(5 \div \frac{15}{34}\\)

Explanation:

Problem 4: $\boldsymbol{\frac{3}{8} \div \frac{5}{6}}$

Step1: Recall fraction division rule

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, $\frac{3}{8} \div \frac{5}{6} = \frac{3}{8} \times \frac{6}{5}$.

Step2: Multiply numerators and denominators

Multiply the numerators: $3 \times 6 = 18$. Multiply the denominators: $8 \times 5 = 40$. So we have $\frac{18}{40}$.

Step3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor, which is 2. $\frac{18 \div 2}{40 \div 2} = \frac{9}{20}$.

Step1: Apply fraction division rule

Multiply by the reciprocal: $\frac{5}{6} \div \frac{3}{8} = \frac{5}{6} \times \frac{8}{3}$.

Step2: Multiply numerators and denominators

Numerators: $5 \times 8 = 40$. Denominators: $6 \times 3 = 18$. Result is $\frac{40}{18}$.

Step3: Simplify the fraction

GCD of 40 and 18 is 2. $\frac{40 \div 2}{18 \div 2} = \frac{20}{9}$ (or $2\frac{2}{9}$).

Step1: Rewrite 9 as a fraction

9 can be written as $\frac{9}{1}$. Then, apply the division rule: $\frac{6}{11} \div \frac{9}{1} = \frac{6}{11} \times \frac{1}{9}$.

Step2: Multiply numerators and denominators

Numerators: $6 \times 1 = 6$. Denominators: $11 \times 9 = 99$. We get $\frac{6}{99}$.

Step3: Simplify the fraction

GCD of 6 and 99 is 3. $\frac{6 \div 3}{99 \div 3} = \frac{2}{33}$.

Answer:

$\frac{9}{20}$

Problem 5: $\boldsymbol{\frac{5}{6} \div \frac{3}{8}}$