Question Video: Simplifying Quotients of Mixed Numbers Mathematics • 6th Grade

Which of the following is equal to (6 1/4)/(2 1/4) [A] 100/36 [B] 28/12 [C] 18/50 [D] 27/50.

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Video Transcript

Which of the following is equal to six and a quarter divided by two and a quarter? Is it A) 100 divided by 36, B) 28 divided by 12, C) 18 divided by 50, or D) 27 divided by 50.

We can immediately eliminate two of our possible answers by looking at the initial fraction. The numerator six and a quarter is greater than the denominator two and a quarter. This means that our equivalent or equal fraction must also have a numerator greater than a denominator or be an improper fraction.

As the only improper fractions here are A and B, we can eliminate C and D. In order to simplify the fraction, we need to convert the numerator and the denominator from mixed fractions into improper fractions. Six whole ones is equal to 24 quarters. Adding the extra quarter gives us 25 quarters or 25 divided by four.

A quicker way to convert from a mixed fraction to an improper fraction is to multiply six by four, which gives us 24, and then add the numerator, in this case one, to give us 25. Either way, it is clear that six and a quarter is the same as 25 quarters.

We now need to do the same thing for the denominator: two and a quarter. Two multiplied by four, the denominator, is equal to eight. And eight plus the numerator, one, equals nine. Therefore, two and a quarter is equal to nine quarters, nine over four or nine divided by four.

Rewriting the numerator and the denominator as improper fractions gives us 25 quarters divided by nine quarters. Multiplying the numerator and the denominator by four then gives us 25 over nine.

Whilst this isn’t one of our options, multiplying the numerator and denominator again by four gives us one 100 over 36, 100 divided by 36. Therefore, the correct answer was answer A. Six and a quarter divided by two and a quarter is equal to or equivalent to 100 divided by 36.

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