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.
