QuestionFind the simplest form of the quotient: $\frac{3}{4} \div \frac{5}{16}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the quotient of $\frac{3}{4}$ divided by $\frac{5}{16}$ in simplest form. . We are given four options $\frac{15}{64}$ , $\frac{15}{16}$ , $\frac{}{5}$ , and $\frac{}{20}$ .

STEP 2

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{}{4} \div \frac{5}{16} = \frac{}{4} \times \frac{16}{5}$

STEP 3

Next, we multiply the numerators (top numbers) of the fractions to get the new numerator, and the denominators (bottom numbers) to get the new denominator.
$\frac{3}{} \times \frac{16}{5} = \frac{3 \times16}{ \times5}$

STEP 4

Perform the multiplication in the numerator and the denominator.
$\frac{3 \times16}{4 \times} = \frac{48}{20}$

STEP 5

Now, we simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is4.
$\frac{48}{20} = \frac{48 \div4}{20 \div4} = \frac{12}{5}$

STEP 6

We can convert this improper fraction to a mixed number by dividing the numerator by the denominator.
$12 \div5 =2 \text{ remainder }2$ So, $\frac{12}{5} =2 \frac{2}{5}$ The quotient of $\frac{3}{4}$ divided by $\frac{5}{16}$ in simplest form is $2 \frac{2}{5}$ .

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