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QuestionFind the total sugar in tons from 2382 \frac{3}{8} containers, each holding 3153 \frac{1}{5} tons. Express as a mixed number.

Studdy Solution

STEP 1

Assumptions1. The shipment of sugar fills 38 \frac{3}{8} containers. . Each container holds 3153 \frac{1}{5} tons of sugar.

STEP 2

First, we need to convert the mixed numbers to improper fractions to make the calculation easier. 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

Let's convert the number of containers to an improper fraction.
Number of Containers=2×8+3=19/8\text{Number of Containers} =2 \times8 +3 =19/8

STEP 4

Next, convert the tons of sugar per container to an improper fraction.
Tons of Sugar per Container=3×+1=16/\text{Tons of Sugar per Container} =3 \times +1 =16/

STEP 5

Now that we have both values as improper fractions, we can multiply them to find the total amount of sugar in the shipment. The formula to multiply fractions isProduct=umerator1×umerator2Denominator1×Denominator2\text{Product} = \frac{\text{umerator}_1 \times \text{umerator}_2}{\text{Denominator}_1 \times \text{Denominator}_2}

STEP 6

Plug in the values for the number of containers and the tons of sugar per container into the formula.
Total Sugar=19×168×5\text{Total Sugar} = \frac{19 \times16}{8 \times5}

STEP 7

Perform the multiplication in the numerator and the denominator.
Total Sugar=30440\text{Total Sugar} = \frac{304}{40}

STEP 8

implify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is8.
Total Sugar=304÷840÷8\text{Total Sugar} = \frac{304 \div8}{40 \div8}

STEP 9

Perform the division to get the total sugar in simplest form.
Total Sugar=385\text{Total Sugar} = \frac{38}{5}

STEP 10

Finally, convert the improper fraction back to a mixed number. The formula to convert an improper fraction to a mixed number isMixed Number=Whole Number+RemainderDenominator\text{Mixed Number} = \text{Whole Number} + \frac{\text{Remainder}}{\text{Denominator}}

STEP 11

Perform the division to find the whole number and the remainder.
Total Sugar=7+35\text{Total Sugar} =7 + \frac{3}{5}The total amount of sugar in the shipment is 7357 \frac{3}{5} tons.

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