QuestionFind the quotient by multiplying by the reciprocal: $\frac{9}{10} \div \frac{12}{7}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the division problem $\frac{9}{10} \div \frac{12}{7}$ . . We are allowed to replace the divisor with its reciprocal and multiply to find the quotient.

STEP 2

First, we need to find the reciprocal of the divisor. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
$Reciprocal\, of\, \frac{12}{7} = \frac{7}{12}$

STEP 3

Now, replace the division operation with multiplication and the divisor with its reciprocal.
$\frac{9}{10} \div \frac{12}{7} = \frac{9}{10} \times \frac{7}{12}$

STEP 4

Next, multiply the two fractions. To do this, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
$\frac{9}{10} \times \frac{7}{12} = \frac{9 \times7}{10 \times12}$

STEP 5

Calculate the numerator and the denominator of the resulting fraction.
$\frac{9 \times7}{10 \times12} = \frac{63}{120}$

STEP 6

Finally, simplify the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor, which is3.
$\frac{63}{120} = \frac{63 \div3}{120 \div3} = \frac{21}{40}$ So, the quotient of $\frac{9}{10} \div \frac{12}{}$ is $\frac{21}{40}$ .

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