Question

Multiply or divide as indicated. Write answers in lowest terms as needed. 212÷1572\frac{1}{2} \div 1\frac{5}{7}

Accepted Answer

First, convert the mixed numbers to improper fractions. For 2(1/2), multiply the whole number 2 by the denominator 2 and add the numerator 1: $$2 	imes 2 + 1 = 5$$, so $$2(1/2) = \frac{5}{2}. $$For 1(5/7), multiply the whole number 1 by the denominator 7 and add the numerator 5: $$1 	imes 7 + 5 = 12$$, so $$1(5/7) = \frac{12}{7}. $$Rewrite the original expression using the improper fractions: $$\frac{5}{2} \div \frac{12}{7}. $$Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, rewrite the division as multiplication by flipping the second fraction: $$\frac{5}{2} 	imes \frac{7}{12}. $$Multiply the numerators together and the denominators together: numerator $$5 	imes 7 = 35$$, denominator $$2 	imes 12 = 24$$, so the product is $$\frac{35}{24}. $$Simplify the fraction $$\frac{35}{24} if $$possible by finding the greatest common divisor (GCD) of 35 and 24 and dividing numerator and denominator by it. If no common factors other than 1 exist, the fraction is already in lowest terms.

Multiply or divide as indicated. Write answers in lowest terms as needed. $2 and one half divided by 1 and five sevenths$

Verified video answer for a similar problem:

Key Concepts

Mixed Numbers and Improper Fractions

Division of Fractions

Simplifying Fractions

Multiply or divide as indicated. Write answers in lowest terms as needed. 212÷1572\(\frac{1}{2}\) \(\div\) 1\(\frac{5}{7}\)