Mike’s mom made a batch of soup that was 5 4/10 cups. each serving was 6/10 cups. how many servings of soup did mike’s mom make?

change 5 4/10 to an improper fraction  (10*5 +4)/10 = 54/10

54/10 divided by 6/10

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54/10* 10/6

54/6

9

There are 9 servings of soup

9 servings

Step-by-step explanation:

(5.4 c)/(0.6c/serving) = 9 serving

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This problem is worked easily in its decimal form, especially if you know your times tables: 6×9 = 54.

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If you want to work it using fractions, you can get to the same place.

5 4/10 = 54/10

Then ...

... (54/10 cups) = (6/10 cups/serving) × (number of servings)

Dividing by the coefficient of (number of servings), we have

... (54/10 cups)/(6/10 cups/serving) = (number of servings)

... (54/10)/(6/10) servings = 54/6 servings = 9 servings = (number of servings)

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Dividing Fractions

You may recall there are a couple of ways to divide fractions:

1. "Invert and multiply"

... (a/b) / (c/d) = (a/b) × (d/c) = (ad)/(bc)

2. Drop the identical denominator (used in this problem)

... (a/b) / (c/b) = a/c . . . . . . both fractions have denominator 'b'

Please note that the first version gives the same result when the denominators are the same: (a/b) / (c/b) = (a/b) × (b/c) = (ab)/(cb) = a/c.

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You may note that the units fraction is divided the same way.