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Shelagh and Luana realize that they could express their ages

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more specifically if they used fractions.

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Doing this will allow them to calculate the difference in

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their ages more precisely.

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If Shelagh describes her age as 15 and 1/2 years old and

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Luana is 7 and 7/12-- I'm assuming years old-- what is

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the difference in their ages?

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Write the answer as a simplified mixed number.

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So Shelagh is older, so she's 15 and 1/2 years old, so we

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literally want to find the difference between 15 and 1/2

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and 7 and 7/12.

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Now we can see immediately-- or maybe it's not obvious to

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you, but 1/2 is the same thing is 6/12, which

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is a less than 7/12.

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So if we separated out the whole number parts and the

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fraction parts, this fraction is actually smaller.

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The 1/2 is smaller than the 7/12, so it might be easier to

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just do this as mixed numbers so we don't have to do all of

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that borrowing and regrouping.

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So let's write both of them as mixed numbers.

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So we have 1 and 1/2.

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We're still going to-- sorry, let's write both of them as

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improper fractions, so we're going to keep 2 in the

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denominator.

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And as an improper fraction, 2 times 15 is 30 plus 1 is 31.

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So 31/2 the same thing as 15 and 1/2, so these are

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equivalent.

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And then 7 and 7/12, if we write it as an improper

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fraction, so we're still going to have the minus sign out

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there, the denominator is 12.

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12 times 7 is 84.

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84 plus 7 is 91.

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It is 91.

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Did I do that right?

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91.

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Yep, that looks right.

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91/12.

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Now, we've written both of them as improper fractions,

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but we still have different denominators, so we have to

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have a common denominator.

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So what is the least common multiple of 2 and 12, or

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what's the smallest number that's

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divisible by both of them?

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Well, 12 is divisible by 12, and 12 is also divisible by 2,

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so 12 is the least common multiple.

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So we want both of them to be over 12.

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And this fraction already is over 12 so we don't have to

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change it: 91/12.

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Now, on the blue one, to go from 2 to 12 in the

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denominator, we have to multiply by 6, so we also have

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to multiply by 6 in the numerator.

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So if we multiply 31 by 6, what do we get?

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You can even do this in your head.

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6 times 30 is 180, 6 times 1 is 6, so it's going to be 186.

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And now we subtract.

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So the difference in their ages is going to be-- the

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denominator is going to be 12.

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It's going to be 186 minus 91, which is equal to-- over 12.

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Let's see, 186 minus just 90 would be 96, but we're

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subtracting 91, so it's going to be 95.

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95, right?

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6 minus 1 is 5, and then 180 minus 90 is 90,

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so that works out.

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So the way we've expressed it right now, it isn't is an

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improper fraction, but they want us to write it as a

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simplified mixed number, so let's do that.

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So how many times does 12 go into 95?

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Let's see, 8 times 12 is 96, so that's too big, so 12 goes

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seven times.

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So this is equal to 7.

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And if we take-- well, let me write it out.

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We don't want to do too much in our head.

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If we go 12 into 95, I'm saying it goes seven times.

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So if that's true, if that's the largest number, then the

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remainder should be less than 12.

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7 times 12 we know is 84 from our times tables, or you could

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just think it's going to be 14 plus 10 times 7, which is 70.

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Either way.

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And let's see, 95 minus 84: 5 minus 4 is 1, 9 minus 8 is 1,

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so we have a remainder of 11.

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So 12 goes into 95 seven times.

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You get 7 wholes and you have 11 left over.

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So 95/12 is 7 and 11/12.

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And we're done!

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The difference between Shelagh and Luana's age is 7 and

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11/12, or Shelagh is 7 and 11/12 years older than Luana.

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