Full solution

Q. Divide. Write the quotient in lowest terms.

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\frac{5}{8} \div 1 \frac{1}{3}=

Convert to improper fraction: Convert the mixed number to an improper fraction. $\newline$ $1 \frac{1}{3}$ is a mixed number. To convert it to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. Then place the result over the original denominator. $\newline$ $1 \times 3 + 1 = 3 + 1 = 4$ $\newline$ So, $1 \frac{1}{3}$ as an improper fraction is $\frac{4}{3}$ .
Take reciprocal and rewrite as multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction. $\newline$ To divide by a fraction, you multiply by its reciprocal. The reciprocal of $\frac{4}{3}$ is $\frac{3}{4}$ . $\newline$ So, $\frac{5}{8}$ $\div$ $\frac{4}{3}$ becomes $\frac{5}{8}$ $\cdot$ $\frac{3}{4}$ .
Multiply numerators and denominators: Multiply the numerators and then the denominators. $\newline$ Multiply the numerators: $5 \times 3 = 15$ $\newline$ Multiply the denominators: $8 \times 4 = 32$ $\newline$ So, $(\frac{5}{8}) \times (\frac{3}{4}) = \frac{15}{32}$ .
Simplify the fraction: Simplify the fraction, if possible. $\newline$ Check if the numerator and denominator have any common factors that can be divided out. In this case, $15$ and $32$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.