Video: Solving Word Problems Involving the Multiplicative Comparison of Two Mixed Numbers

Scarlett and Daniel went out to get some ice cream. Scarlett had 4/7 pt of chocolate chip ice cream, while Daniel had 2/3 pt of strawberry flavored ice cream. Determine how many times as much ice cream Daniel had as Scarlett.

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Video Transcript

Scarlett and Daniel went out to get to some ice cream. Scarlett had four-sevenths of a pint of chocolate chip ice cream, while Daniel had two-thirds of a pint of strawberry-flavoured ice cream. Determine how many times as much ice cream Daniel had as Scarlett.

There are a few methods we could use to solve this problem. We will look at two of them. We’re told that Daniel had more ice cream than Scarlett. Therefore, Scarlett’s amount multiplied by some number will give us Daniel’s amount. Scarlett had four-sevenths of a pint of ice cream. Whereas Daniel had two-thirds of a pint. This means that four-sevenths multiplied by some number, we will call 𝑥, is equal to two-thirds. Dividing both sides of this equation by four-sevenths gives us 𝑥 is equal to two-thirds divided by four-sevenths.

When dividing a fraction by another fraction, we need to multiply by the reciprocal of the second fraction. This is often called K C F. We keep the first fraction the same. The division sign changes to a multiplication sign. We flip the second fraction as the reciprocal of any fraction is the fraction upside down. We can now multiply two-thirds by seven-quarters by multiplying the numerators and then multiplying the denominators. This is equal to 14 over 12 or fourteen twelfths.

Simplifying this fraction by dividing the numerator and denominator by two gives us seven-sixths. The line in a fraction means divide, so we can divide seven by six. This is equal to one remainder one. Therefore, seven-sixths is the same as one and one-sixth. We can therefore conclude that Daniel has one and one-sixth as much ice cream as Scarlett.

We will now look at an alternative method by comparing the two fractions. We know that Scarlett had four-sevenths of a pint of ice cream and Daniel had two-thirds of a pint. In order to compare fractions, it is useful to make the denominators the same. The lowest common multiple of seven and three is 21. Multiplying the top and bottom of Scarlett’s fraction by three gives us 12 over 21. Multiplying the top and bottom of Daniel’s fraction by seven gives us 14 out of 21.

As the denominators are now the same, we can say that the ratio of ice cream of Daniel to Scarlett is 14 to 12. This ratio can be simplified by dividing both sides by two. For every seven parts of ice cream Daniel has, Scarlett has six parts. Once again, we see that Daniel had seven-sixths times as much ice cream as Scarlett. As already shown, this is the same as one and one-sixth. This is an alternative method that can be used to work out how many times bigger one fraction is than another.

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