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If Noah’s son is 6.75 years old, express his age as a mixed number in the simplest form.
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We’re given the age of Noah’s son as a decimal.
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We’re told that he’s 6.75 years old.
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We know the decimals have a whole number part and a part that’s worth less than one.
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In 6.75, the whole number part is six, six ones.
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This is the number of whole years in our son’s age.
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And as we said there’s a part that’s worth less than zero.
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In this decimal, it’s 0.75 or 75 hundredths.
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We’re asked to express Noah’s son’s age, not as a decimal, but as a mixed number.
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If we remind ourselves, a mixed number is a number that’s made up of a whole number and a fraction.
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So something like two and a half is a mixed number.
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The whole number part is the number two.
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And then there’s a fraction on the end; in this case, it’s one half.
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This part is less than one.
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So we need to convert 6.75 into a mixed number.
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We already know the whole number part of our mixed number is going to be six.
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But how can we write 0.75, which is the part that’s worth less than one, as a fraction?
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0.75 is the same as 75 hundredths.
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So we could write Noah’s son’s age as six and 75 hundredths.
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But we are asked to express the mixed number in the simplest form.
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Can we make the fraction any simpler than it already is?
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What can we divide both 75 and 100 by?
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Both numbers are divisible by 25.
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There are three 25s in 75, and there are four 25s in 100.
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So 75 hundredths or 0.75 is the same as three-quarters.
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You may have known that already.
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Noah’s son’s age as a decimal is 6.75 years old.
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And we decided that we could write this as a mixed number as six and 75 hundredths.
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By dividing both the numerator and denominator by 25, we were able to simplify the fraction part of the mixed number.
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In its simplest form, Noah’s son’s age is six and three-quarters.