Dividing Mixed Numbers

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Dividing mixed numbers helps in understanding of dividing mixed fractions. Any fraction that is in the form of whole number and fraction is a mixed fraction. To divide mixed number first convert mixed fractions into improper fractions. Then invert the fraction that is divisor and multiply with the fraction in the numerator. Multiply the numerators together and denominators together. If possible simplify the answer and convert into mixed fraction if needed.
The following examples clearly illustrate the steps on dividing mixed numbers.

Example 1: Peter is cutting a roll of cookie dough into pieces that is 1 ½ inch thick each. How many pieces can be made if roll is 12 ½ inches long?

Solution: Length of roll = 12 ½

Cookie thickness= 1 ½

Divide length of roll by thickness of cookie to find number of cookies to be made.

12 ½ / 1 ½ = (25/2) / (3/2)

Put reciprocal of divisor and multiply with the fraction

(25/2) / (3/2) = (25/2) * (2/3) = 50 / 6 = 25/3

25/3 is an improper fraction so convert it into mixed number 25/3 = 8 1/3

Therefore, 8 1/3 pieces can be made.

Example 2: Felicia can run 18 ½ miles in 1 ¼ hours. How many miles per hour can she run?

Solution: Total miles she can run = 18 ½ miles

Time taken =1 ¼ hours

Miles she can run in one hour = total miles / time taken

Miles in one hour = (18 ½) / (1 ¼) = (37/2) / (5/4) = (37/2) * (4/5) = 148 / 10

Simplify it 148 / 10 = 74/5 = 14 4/5 miles

She can run 14 4/5 miles in one hour.

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