QuestionCalculate: $165 \frac{1}{4} \div 41 \frac{1}{4} =$

Studdy Solution

STEP 1

Assumptions1. We are given two mixed numbers, $165 \frac{1}{4}$ and $41 \frac{1}{4}$ . . We need to divide the first mixed number by the second one.

STEP 2

First, we need to convert the mixed numbers into improper fractions. 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, apply the formula to the first mixed number $165 \frac{1}{}$ .
$\text{Improper Fraction} = (165 \times) +1$

STEP 4

Calculate the improper fraction for the first mixed number.
$\text{Improper Fraction} = (165 \times4) +1 =661$ So, $165 \frac{1}{4}$ can be written as $\frac{661}{4}$ .

STEP 5

Repeat the same process for the second mixed number $41 \frac{1}{4}$ .
$\text{Improper Fraction} = (41 \times4) +1$

STEP 6

Calculate the improper fraction for the second mixed number.
$\text{Improper Fraction} = (41 \times4) +1 =165$ So, $41 \frac{1}{4}$ can be written as $\frac{165}{4}$ .

STEP 7

Now, we need to divide the first improper fraction by the second one. The formula for dividing fractions is $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

STEP 8

Apply the formula to our problem.
$\frac{661}{4} \div \frac{165}{4} = \frac{661}{4} \times \frac{4}{165}$

STEP 9

implify the equation.
$\frac{661}{4} \times \frac{4}{165} = \frac{661}{165}$

STEP 10

implify the fraction.
$\frac{661}{165} =4$ So, $165 \frac{}{4} \div41 \frac{}{4} =4$ .

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