Math

QuestionFind the quotient by multiplying by the reciprocal: 110÷32\frac{1}{10} \div \frac{3}{2}.

Studdy Solution

STEP 1

Assumptions1. We are dividing two fractions 110\frac{1}{10} and 3\frac{3}{}. . We will use the method of replacing the divisor with its reciprocal and multiplying.

STEP 2

First, we need to find the reciprocal of the divisor. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
Reciprocalof2=2Reciprocal\, of\, \frac{}{2} = \frac{2}{}

STEP 3

Now, we replace the divisor 32\frac{3}{2} with its reciprocal 23\frac{2}{3} and change the division operation to multiplication.
110÷32=110×23\frac{1}{10} \div \frac{3}{2} = \frac{1}{10} \times \frac{2}{3}

STEP 4

Next, we multiply the two fractions. To do this, we multiply the numerators together to get the new numerator, and the denominators together to get the new denominator.
110×23=1×210×3\frac{1}{10} \times \frac{2}{3} = \frac{1 \times2}{10 \times3}

STEP 5

Calculate the multiplication of the numerators and the denominators.
1×210×3=230\frac{1 \times2}{10 \times3} = \frac{2}{30}

STEP 6

Finally, we simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is2.
230=2÷230÷2\frac{2}{30} = \frac{2 \div2}{30 \div2}

STEP 7

Calculate the simplified fraction.
2÷230÷2=115\frac{2 \div2}{30 \div2} = \frac{1}{15}So, the quotient of 110\frac{1}{10} divided by 32\frac{3}{2} is 115\frac{1}{15}.

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