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QuestionDivide and simplify: 413÷8234 \frac{1}{3} \div 8 \frac{2}{3}. What is the answer in whole number or simplified fraction form?

Studdy Solution

STEP 1

Assumptions1. We are dividing two mixed numbers. . The mixed numbers are 4134 \frac{1}{3} and 838 \frac{}{3}.
3. We need to simplify the answer.

STEP 2

First, we need to convert the mixed numbers into improper fractions. The formula for converting a mixed number to an improper fraction isImproper Fraction=Whole Number×Denominator+umerator\text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{umerator}

STEP 3

Convert 13 \frac{1}{3} to an improper fraction.
×3+13=133\frac{ \times3 +1}{3} = \frac{13}{3}

STEP 4

Convert 8238 \frac{2}{3} to an improper fraction.
8×3+23=263\frac{8 \times3 +2}{3} = \frac{26}{3}

STEP 5

Now, we have two improper fractions 133\frac{13}{3} and 263\frac{26}{3}. We can divide these fractions by multiplying the first fraction by the reciprocal of the second fraction.
133÷263=133×326\frac{13}{3} \div \frac{26}{3} = \frac{13}{3} \times \frac{3}{26}

STEP 6

Multiply the fractions.
133×326=13×33×26=3978\frac{13}{3} \times \frac{3}{26} = \frac{13 \times3}{3 \times26} = \frac{39}{78}

STEP 7

Now, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it.
The GCD of39 and78 is39.
3978=39÷3978÷39=12\frac{39}{78} = \frac{39 \div39}{78 \div39} = \frac{1}{2}The simplified fraction is 12\frac{1}{2}.

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