Divide. Write the quotient in lowest terms. $\newline$ $5 \div 3 \frac{1}{3}=$

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Q. Divide. Write the quotient in lowest terms.

\newline

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

Identify numbers involved: Identify the numbers involved in the division. $\newline$ We have the whole number $5$ and the fraction $3\frac{1}{3}$ , which is a mixed number.
Convert to improper fraction: Convert the mixed number to an improper fraction. $\newline$ $3\frac{1}{3}$ can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator, then placing the result over the original denominator. $\newline$ $3\frac{1}{3} = (3 \times 3 + 1) / 3 = \frac{10}{3}$
Rewrite division problem: Rewrite the division problem using the improper fraction. $\newline$ Now the division problem is $5 \div \left(\frac{10}{3}\right)$ .
Convert to multiplication problem: Convert the division problem to a multiplication problem. $\newline$ To divide by a fraction, we multiply by its reciprocal. $\newline$ $5 \div \left(\frac{10}{3}\right) = 5 \times \left(\frac{3}{10}\right)$
Perform the multiplication: Perform the multiplication. $\newline$ Now we multiply the numerators and the denominators separately. $\newline$ $5 \times 3 = 15$ $\newline$ $1 \times 10 = 10$ $\newline$ So, $5 \times \left(\frac{3}{10}\right) = \frac{15}{10}$
Simplify to lowest terms: Simplify the fraction to its lowest terms. $\newline$ $\frac{15}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $5$ . $\newline$ $15 \div 5 = 3$ $\newline$ $10 \div 5 = 2$ $\newline$ So, $\frac{15}{10}$ simplified to lowest terms is $\frac{3}{2}$ .