Divide. Write the quotient in lowest terms. 3(3)/(10)÷1(4)/(7)=

Rewrite mixed numbers as improper fractions: Rewrite the mixed numbers as improper fractions. 3(3)/(10) can be rewritten as (30 + 3)/10 = 33/10. 1(4)/(7) can be rewritten as (7 + 4)/7 = 11/7.Rewrite division as multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction. The expression 33/10 ÷ 11/7 can be rewritten as 33/10 * 7/11.Multiply numerators and denominators: Multiply the numerators and the denominators. (33 * 7)/(10 * 11) = 231/110.Simplify fraction using GCF: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and the denominator. The GCF of 231 and 110 is 1, so the fraction is already in its simplest form.Check for further simplification: Check if the fraction can be simplified further. Since the numerator and the denominator have no common factors other than 1, the fraction 231/110 is already in its simplest form.

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Algebra 2

Multiply and divide rational expressions

Full solution

Q. Divide. Write the quotient in lowest terms.

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3 \frac{3}{10} \div 1 \frac{4}{7}=

Rewrite mixed numbers as improper fractions: Rewrite the mixed numbers as improper fractions. $\newline$ $3\left(\frac{3}{10}\right)$ can be rewritten as $\frac{30 + 3}{10} = \frac{33}{10}$ . $\newline$ $1\left(\frac{4}{7}\right)$ can be rewritten as $\frac{7 + 4}{7} = \frac{11}{7}$ .
Rewrite division as multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction. $\newline$ The expression $\frac{33}{10} \div \frac{11}{7}$ can be rewritten as $\frac{33}{10} \times \frac{7}{11}$ .
Multiply numerators and denominators: Multiply the numerators and the denominators. $\newline$ $(33 \times 7)/(10 \times 11) = 231/110$ .
Simplify fraction using GCF: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and the denominator. $\newline$ The GCF of $231$ and $110$ is $1$ , so the fraction is already in its simplest form.
Check for further simplification: Check if the fraction can be simplified further. $\newline$ Since the numerator and the denominator have no common factors other than $1$ , the fraction $\frac{231}{110}$ is already in its simplest form.