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- Shelagh and Luana realize that they could express their ages
- more specifically if they used fractions.
- Doing this will allow them to calculate the difference in
- their ages more precisely.
- If Shelagh describes her age as 15 and 1/2 years old and
- Luana is 7 and 7/12-- I'm assuming years old-- what is
- the difference in their ages?
- Write the answer as a simplified mixed number.
- So Shelagh is older, so she's 15 and 1/2 years old, so we
- literally want to find the difference between 15 and 1/2
- and 7 and 7/12.
- Now we can see immediately-- or maybe it's not obvious to
- you, but 1/2 is the same thing is 6/12, which
- is a less than 7/12.
- So if we separated out the whole number parts and the
- fraction parts, this fraction is actually smaller.
- The 1/2 is smaller than the 7/12, so it might be easier to
- just do this as mixed numbers so we don't have to do all of
- that borrowing and regrouping.
- So let's write both of them as mixed numbers.
- So we have 1 and 1/2.
- We're still going to-- sorry, let's write both of them as
- improper fractions, so we're going to keep 2 in the
- denominator.
- And as an improper fraction, 2 times 15 is 30 plus 1 is 31.
- So 31/2 the same thing as 15 and 1/2, so these are
- equivalent.
- And then 7 and 7/12, if we write it as an improper
- fraction, so we're still going to have the minus sign out
- there, the denominator is 12.
- 12 times 7 is 84.
- 84 plus 7 is 91.
- It is 91.
- Did I do that right?
- 91.
- Yep, that looks right.
- 91/12.
- Now, we've written both of them as improper fractions,
- but we still have different denominators, so we have to
- have a common denominator.
- So what is the least common multiple of 2 and 12, or
- what's the smallest number that's
- divisible by both of them?
- Well, 12 is divisible by 12, and 12 is also divisible by 2,
- so 12 is the least common multiple.
- So we want both of them to be over 12.
- And this fraction already is over 12 so we don't have to
- change it: 91/12.
- Now, on the blue one, to go from 2 to 12 in the
- denominator, we have to multiply by 6, so we also have
- to multiply by 6 in the numerator.
- So if we multiply 31 by 6, what do we get?
- You can even do this in your head.
- 6 times 30 is 180, 6 times 1 is 6, so it's going to be 186.
- And now we subtract.
- So the difference in their ages is going to be-- the
- denominator is going to be 12.
- It's going to be 186 minus 91, which is equal to-- over 12.
- Let's see, 186 minus just 90 would be 96, but we're
- subtracting 91, so it's going to be 95.
- 95, right?
- 6 minus 1 is 5, and then 180 minus 90 is 90,
- so that works out.
- So the way we've expressed it right now, it isn't is an
- improper fraction, but they want us to write it as a
- simplified mixed number, so let's do that.
- So how many times does 12 go into 95?
- Let's see, 8 times 12 is 96, so that's too big, so 12 goes
- seven times.
- So this is equal to 7.
- And if we take-- well, let me write it out.
- We don't want to do too much in our head.
- If we go 12 into 95, I'm saying it goes seven times.
- So if that's true, if that's the largest number, then the
- remainder should be less than 12.
- 7 times 12 we know is 84 from our times tables, or you could
- just think it's going to be 14 plus 10 times 7, which is 70.
- Either way.
- And let's see, 95 minus 84: 5 minus 4 is 1, 9 minus 8 is 1,
- so we have a remainder of 11.
- So 12 goes into 95 seven times.
- You get 7 wholes and you have 11 left over.
- So 95/12 is 7 and 11/12.
- And we're done!
- The difference between Shelagh and Luana's age is 7 and
- 11/12, or Shelagh is 7 and 11/12 years older than Luana.