Divide. Write the quotient in lowest terms. (3)/(5)÷2(1)/(2)=

Convert to Improper Fraction: Convert the mixed number to an improper fraction. 2(1)/(2) is a mixed number. To convert it to an improper fraction, multiply the whole number by the denominator and add the numerator. Then place the result over the original denominator. 2(1)/(2) = (2*2 + 1)/2 = (4 + 1)/2 = 5/2Multiply by Reciprocal: Rewrite the division problem as multiplication by the reciprocal of the divisor. To divide by a fraction, multiply by its reciprocal. The reciprocal of 5/2 is 2/5. (3/5) ÷ (5/2) = (3/5) * (2/5)Multiply Numerators and Denominators: Multiply the numerators and then the denominators. Multiply the numerators: 3 * 2 = 6 Multiply the denominators: 5 * 5 = 25 So, (3/5) * (2/5) = 6/25Simplify Fraction: Simplify the fraction if possible. Check if the fraction 6/25 can be simplified. Since 6 and 25 have no common factors other than 1, the fraction is already in its simplest form.

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Algebra 2

Multiply and divide rational expressions

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Q. Divide. Write the quotient in lowest terms.

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\frac{3}{5} \div 2 \frac{1}{2}=

Convert to Improper Fraction: Convert the mixed number to an improper fraction. $2\left(\frac{1}{2}\right)$ is a mixed number. To convert it to an improper fraction, multiply the whole number by the denominator and add the numerator. Then place the result over the original denominator. $2\left(\frac{1}{2}\right) = \left(2\times2 + 1\right)/2 = \left(4 + 1\right)/2 = 5/2$
Multiply by Reciprocal: Rewrite the division problem as multiplication by the reciprocal of the divisor. $\newline$ To divide by a fraction, multiply by its reciprocal. The reciprocal of $\frac{5}{2}$ is $\frac{2}{5}$ . $\newline$ $\frac{3}{5}$ $\div$ $\frac{5}{2}$ = $\frac{3}{5}$ $*$ $\frac{2}{5}$
Multiply Numerators and Denominators: Multiply the numerators and then the denominators. $\newline$ Multiply the numerators: $3 \times 2 = 6$ $\newline$ Multiply the denominators: $5 \times 5 = 25$ $\newline$ So, $(\frac{3}{5}) \times (\frac{2}{5}) = \frac{6}{25}$
Simplify Fraction: Simplify the fraction if possible. $\newline$ Check if the fraction $\frac{6}{25}$ can be simplified. Since $6$ and $25$ have no common factors other than $1$ , the fraction is already in its simplest form.