Studdy AI Logo
Math

QuestionMultiply 5165 \frac{1}{6} by 8568 \frac{5}{6} and simplify your answer.

Studdy Solution

STEP 1

Assumptions1. We are multiplying two mixed numbers. . We need to simplify the answer to a whole number, proper fraction, or mixed number.

STEP 2

First, we need to convert the mixed numbers into improper fractions. The formula to convert 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 the first mixed number, 5165 \frac{1}{6}, to an improper fraction.
Improper Fraction=5×6+1=31/6\text{Improper Fraction} =5 \times6 +1 =31/6

STEP 4

Convert the second mixed number, 868 \frac{}{6}, to an improper fraction.
Improper Fraction=8×6+=53/6\text{Improper Fraction} =8 \times6 + =53/6

STEP 5

Now, we multiply the two improper fractions. The formula to multiply fractions isab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

STEP 6

Multiply the two improper fractions.
316×536=31×536×6\frac{31}{6} \times \frac{53}{6} = \frac{31 \times53}{6 \times6}

STEP 7

Perform the multiplication.
31×536×6=164336\frac{31 \times53}{6 \times6} = \frac{1643}{36}

STEP 8

Now, we convert the improper fraction back to a mixed number. The formula to convert an improper fraction to a mixed number isWhole Number=umerator divided by Denominator\text{Whole Number} = \text{umerator} \, \text{divided by} \, \text{Denominator}Remainder=umerator modulo Denominator\text{Remainder} = \text{umerator} \, \text{modulo} \, \text{Denominator}Mixed Number=Whole Number+RemainderDenominator\text{Mixed Number} = \text{Whole Number} + \frac{\text{Remainder}}{\text{Denominator}}

STEP 9

Convert the improper fraction 164336\frac{1643}{36} to a mixed number.
Whole Number=1643 divided by 36=45\text{Whole Number} =1643 \, \text{divided by} \,36 =45Remainder=1643 modulo 36=23\text{Remainder} =1643 \, \text{modulo} \,36 =23Mixed Number=45+2336\text{Mixed Number} =45 + \frac{23}{36}So, 56⋅856=4523365 \frac{}{6} \cdot8 \frac{5}{6} =45 \frac{23}{36}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord