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Scarlett and Daniel went out to get to some ice cream.
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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.
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Determine how many times as much ice cream Daniel had as Scarlett.
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There are a few methods we could use to solve this problem.
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We will look at two of them.
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We’re told that Daniel had more ice cream than Scarlett.
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Therefore, Scarlett’s amount multiplied by some number will give us Daniel’s amount.
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Scarlett had four-sevenths of a pint of ice cream.
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Whereas Daniel had two-thirds of a pint.
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This means that four-sevenths multiplied by some number, we will call 𝑥, is equal to two-thirds.
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Dividing both sides of this equation by four-sevenths gives us 𝑥 is equal to two-thirds divided by four-sevenths.
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When dividing a fraction by another fraction, we need to multiply by the reciprocal of the second fraction.
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This is often called K C F.
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We keep the first fraction the same.
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The division sign changes to a multiplication sign.
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We flip the second fraction as the reciprocal of any fraction is the fraction upside down.
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We can now multiply two-thirds by seven-quarters by multiplying the numerators and then multiplying the denominators.
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This is equal to 14 over 12 or fourteen twelfths.
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Simplifying this fraction by dividing the numerator and denominator by two gives us seven-sixths.
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The line in a fraction means divide, so we can divide seven by six.
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This is equal to one remainder one.
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Therefore, seven-sixths is the same as one and one-sixth.
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We can therefore conclude that Daniel has one and one-sixth as much ice cream as Scarlett.
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We will now look at an alternative method by comparing the two fractions.
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We know that Scarlett had four-sevenths of a pint of ice cream and Daniel had two-thirds of a pint.
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In order to compare fractions, it is useful to make the denominators the same.
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The lowest common multiple of seven and three is 21.
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Multiplying the top and bottom of Scarlett’s fraction by three gives us 12 over 21.
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Multiplying the top and bottom of Daniel’s fraction by seven gives us 14 out of 21.
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As the denominators are now the same, we can say that the ratio of ice cream of Daniel to Scarlett is 14 to 12.
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This ratio can be simplified by dividing both sides by two.
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For every seven parts of ice cream Daniel has, Scarlett has six parts.
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Once again, we see that Daniel had seven-sixths times as much ice cream as Scarlett.
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As already shown, this is the same as one and one-sixth.
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This is an alternative method that can be used to work out how many times bigger one fraction is than another.