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Divide. Write the quotient in lowest terms.

(1)/(4)÷1(1)/(8)=

Divide. Write the quotient in lowest terms. $\newline$ $\frac{1}{4} \div 1 \frac{1}{8}=$

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Multiply and divide rational expressions

Full solution

Q. Divide. Write the quotient in lowest terms.

\newline

\frac{1}{4} \div 1 \frac{1}{8}=

Convert to Improper Fraction: Rewrite the mixed number $1\frac{1}{8}$ as an improper fraction. $\newline$ $1\frac{1}{8}$ can be written as $(\frac{8}{8} + \frac{1}{8})$ , which equals $\frac{9}{8}.$
Set up Multiplication Problem: Set up the division problem as a multiplication problem by taking the reciprocal of the second fraction. $\newline$ $(\frac{1}{4}) \div (\frac{9}{8})$ becomes $(\frac{1}{4}) \times (\frac{8}{9})$ .
Multiply Numerators and Denominators: Multiply the numerators and the denominators. $\newline$ $(1 \times 8) / (4 \times 9)$ equals $8/36$ .
Find Greatest Common Divisor: Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. $\newline$ The GCD of $8$ and $36$ is $4$ .
Simplify Fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction to its lowest terms. $\newline$ $(8 \div 4) / (36 \div 4)$ equals $2/9$ .

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