QuestionDivide $1 \frac{1}{2}$ by $\frac{3}{4}$ .

Studdy Solution

STEP 1

Assumptions1. We are given a division problem $1 \frac{1}{} \div \frac{3}{4}$ . . We need to solve this division problem.

STEP 2

First, we need to convert the mixed number $1 \frac{1}{2}$ into an improper fraction. The formula to convert a mixed number into an improper fraction is $\text{Improper Fraction} = (\text{Whole Number} \times \text{Denominator}) + \text{umerator}$

STEP 3

Now, plug in the given values for the whole number, denominator, and numerator to calculate the improper fraction.
$\text{Improper Fraction} = (1 \times2) +1$

STEP 4

Calculate the improper fraction.
$\text{Improper Fraction} = (1 \times2) +1 =3$ So, $1 \frac{1}{2}$ is equivalent to $\frac{3}{2}$ .

STEP 5

Now, we can rewrite the original problem using the improper fraction.
$\frac{3}{2} \div \frac{3}{4}$

STEP 6

The division of fractions is done by multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator. So, the reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$ .

STEP 7

Now, we can rewrite the division problem as a multiplication problem.
$\frac{3}{2} \times \frac{4}{3}$

STEP 8

Multiply the fractions.
$\frac{3}{2} \times \frac{4}{3} = \frac{3 \times4}{2 \times3}$

STEP 9

implify the fraction.
$\frac{3 \times4}{2 \times3} = \frac{12}{6}$

STEP 10

implify the fraction to get the final answer.
$\frac{12}{6} =2$ So, $\frac{}{2} \div \frac{3}{4} =2$ .

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