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Divide. Write the quotient in lowest terms.

5÷3(1)/(3)=

Divide. Write the quotient in lowest terms.\newline5÷313= 5 \div 3 \frac{1}{3}=

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Q. Divide. Write the quotient in lowest terms.\newline5÷313= 5 \div 3 \frac{1}{3}=
  1. Identify numbers involved: Identify the numbers involved in the division.\newlineWe have the whole number 55 and the fraction 3133\frac{1}{3}, which is a mixed number.
  2. Convert to improper fraction: Convert the mixed number to an improper fraction.\newline3133\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.\newline313=(3×3+1)/3=1033\frac{1}{3} = (3 \times 3 + 1) / 3 = \frac{10}{3}
  3. Rewrite division problem: Rewrite the division problem using the improper fraction.\newlineNow the division problem is 5÷(103)5 \div \left(\frac{10}{3}\right).
  4. Convert to multiplication problem: Convert the division problem to a multiplication problem.\newlineTo divide by a fraction, we multiply by its reciprocal.\newline5÷(103)=5×(310)5 \div \left(\frac{10}{3}\right) = 5 \times \left(\frac{3}{10}\right)
  5. Perform the multiplication: Perform the multiplication.\newlineNow we multiply the numerators and the denominators separately.\newline5×3=155 \times 3 = 15\newline1×10=101 \times 10 = 10\newlineSo, 5×(310)=15105 \times \left(\frac{3}{10}\right) = \frac{15}{10}
  6. Simplify to lowest terms: Simplify the fraction to its lowest terms.\newline1510\frac{15}{10} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 55.\newline15÷5=315 \div 5 = 3\newline10÷5=210 \div 5 = 2\newlineSo, 1510\frac{15}{10} simplified to lowest terms is 32\frac{3}{2}.

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