QuestionDivide $1 \frac{1}{6}$ by $2 \frac{5}{8}$ .

Studdy Solution

STEP 1

Assumptions1. We are performing the operation of division between two mixed numbers. . We need to convert the mixed numbers into improper fractions before performing the operation.

STEP 2

First, let's 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

Let's convert the first mixed number, $1 \frac{1}{6}$ , into an improper fraction using the formula.
$\text{Improper Fraction} = (1 \times6) +1$

STEP 4

Calculate the improper fraction for the first mixed number.
$\text{Improper Fraction} =6 +1 =7$ So, $1 \frac{1}{6}$ can be written as $\frac{7}{6}$ .

STEP 5

Now, let's convert the second mixed number, $2 \frac{5}{8}$ , into an improper fraction using the formula.
$\text{Improper Fraction} = (2 \times8) +5$

STEP 6

Calculate the improper fraction for the second mixed number.
$\text{Improper Fraction} =16 +5 =21$ So, $2 \frac{5}{8}$ can be written as $\frac{21}{8}$ .

STEP 7

Now that we have both numbers as improper fractions, we can perform the division. Remember, division of fractions is done by multiplying the first fraction by the reciprocal of the second fraction.
$\frac{7}{6} \div \frac{21}{} = \frac{7}{6} \times \frac{}{21}$

STEP 8

Perform the multiplication operation.
$\frac{7}{6} \times \frac{8}{21} = \frac{56}{126}$

STEP 9

The fraction $\frac{56}{126}$ can be simplified by finding the greatest common divisor (GCD) of56 and126 and dividing both the numerator and the denominator by the GCD.
The GCD of56 and126 is14.

STEP 10

Divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{56}{126} = \frac{56 \div14}{126 \div14} = \frac{4}{9}$ So, $\frac{}{6} \div2 \frac{5}{8} = \frac{4}{9}$ .

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