QuestionMultiply $6 \frac{1}{2}$ by $1 \frac{8}{13}$ and simplify to a mixed number.

Studdy Solution

STEP 1

Assumptions1. We are multiplying two mixed numbers $6 \frac{1}{}$ and $1 \frac{8}{13}$ . The result should be simplified and written as a mixed number

STEP 2

First, we need to convert each mixed number to an improper fraction. The formula to convert a mixed number to an improper fraction is $\text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{umerator}$

STEP 3

Let's convert $6 \frac{1}{2}$ to an improper fraction using the formula.
$\text{Improper Fraction} =6 \times2 +1$

STEP 4

Calculate the improper fraction for $6 \frac{1}{2}$ .
$\text{Improper Fraction} =6 \times2 +1 =13$ So, $6 \frac{1}{2}$ is equivalent to $\frac{13}{2}$ .

STEP 5

Now, let's convert $1 \frac{8}{13}$ to an improper fraction using the same formula.
$\text{Improper Fraction} =1 \times13 +8$

STEP 6

Calculate the improper fraction for $1 \frac{8}{13}$ .
$\text{Improper Fraction} =1 \times13 +8 =21$ So, $1 \frac{8}{13}$ is equivalent to $\frac{21}{13}$ .

STEP 7

Now that we have both numbers as improper fractions, we can multiply them together. The formula to multiply fractions is $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

STEP 8

Substitute the values of the fractions into the formula.
$\frac{13}{2} \times \frac{21}{13} = \frac{13 \times21}{2 \times13}$

STEP 9

implify the multiplication of the fractions.
$\frac{13 \times21}{2 \times13} = \frac{273}{26}$

STEP 10

Now, let's convert the improper fraction back to a mixed number. The formula to convert an improper fraction to a mixed number is $\text{Whole Number} = \text{umerator} \div \text{Denominator}$ $\text{Fraction Part} = \text{umerator} \mod \text{Denominator}$

STEP 11

Substitute the values of the fraction into the formula.
$\text{Whole Number} =273 \div26$ $\text{Fraction Part} =273 \mod26$

STEP 12

Calculate the whole number and the fraction part.
$\text{Whole Number} =273 \div26 =10$ $\text{Fraction Part} =273 \mod26 =$ So, the mixed number is $10 \frac{}{26}$ .
The product of $6 \frac{}{2}$ and $\frac{8}{}$ , simplified and written as a mixed number, is $10 \frac{}{26}$ .

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