Divide and Simplify

Explanation

We will write 120 as a fraction and then multiply the first fraction by the reciprocal of the second fraction.

• Write 120 as a fraction: 120 = \(\frac{120}{1}\)
  • \(120 ÷ \frac{10}{7} = \frac{120}{1} \color{red}{÷ \frac{10}{7}}\)
• Multiply \(\frac{120}{1}\) by the reciprocal of \(\frac{10}{7}\), which is \(\frac{7}{10}\)
  • = \(\frac{120}{1} \color{red}{ \cdot \frac{7}{10}}\)
• Multiply the numerators.  Multiply the denominators.
  • \(\frac{120 \cdot 7}{1 \cdot 10}\)
• To simplify, factor 120 as 10 • 12, then remove the common factor of 10 from the numerator and denominator.
  • \(\require{cancel} \frac{\cancel{10}^1 \cdot 12 \cdot 7}{1 \cdot \cancel{10}_1}\)
• Multiply the remaining factors in the numerator: 1 • 12 • 7 = 84.  Multiply the remaining factors in the denominator: 1 • 1 = 1.
  • = \(\frac{84}{1}\)
• Any whole number divided by 1 is the same number
  • = 84

Because of the relationship between multiplication and division, the sign rules for dividing fractions are the same as those for multiplying fractions.