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Question Multiply 3563 \frac{5}{6} by 12\frac{1}{2}.

Studdy Solution

STEP 1

Assumptions1. We are multiplying two fractions 3563 \frac{5}{6} and 1\frac{1}{}. . 3563 \frac{5}{6} is a mixed number which can be converted into an improper fraction.

STEP 2

First, we need to convert the mixed number 56 \frac{5}{6} into an improper fraction. The formula to convert a mixed number into an improper fraction isImproper Fraction=Whole Number×Denominator+umerator\text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{umerator}

STEP 3

Now, plug in the given values for the whole number, denominator, and numerator to calculate the improper fraction.
Improper Fraction=3×6+5\text{Improper Fraction} =3 \times6 +5

STEP 4

Calculate the improper fraction.
Improper Fraction=3×6+=23\text{Improper Fraction} =3 \times6 + =23So, 363 \frac{}{6} can be written as 236\frac{23}{6}.

STEP 5

Now that we have both fractions as improper fractions, we can multiply them. The formula to multiply two fractions is(ab)×(cd)=a×cb×d(\frac{a}{b}) \times (\frac{c}{d}) = \frac{a \times c}{b \times d}

STEP 6

Now, plug in the given values for a, b, c, and d to calculate the product.
(236)×(12)=23×16×2(\frac{23}{6}) \times (\frac{1}{2}) = \frac{23 \times1}{6 \times2}

STEP 7

Calculate the product.
23×16×2=2312\frac{23 \times1}{6 \times2} = \frac{23}{12}So, 356⋅12=23123 \frac{5}{6} \cdot \frac{1}{2} = \frac{23}{12}.

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