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- Regina rode her bike 2 and 1/4 miles from her house to school
- and then 1 and 5/8 miles to her friend's house.
- How many miles did Regina ride in total?
- So she first rode 2 and 1/4 miles, and then she
- rode 1 and 5/8 miles.
- then she rode 1 and 5/8 miles
- So the sum is the total number of miles she rode.
- So to take this sum, we've seen that we can add the whole
- number parts, because this is really the same thing as 2
- plus 1/4 plus 1 plus 5/8, so we can just switch the order,
- if you want to view it that way.
- So we can add the 2 plus the 1 first, and then we get-- let
- me do that here.
- So 2 plus the 1, you get 3, and then we need to add the
- 1/4 plus 5/8.
- And to add these two fractions, we have to find the
- least common multiple of 4 and 8.
- That'll be our new denominator.
- 8 is divisible by both 8 and 4, so that is the least common
- multiple of 4 and 8, so our common denominator will be 8.
- Obviously, 5/8 will still be 5/8.
- Now to go from a denominator of 4 to 8, you have to
- multiply the denominator by 2, so we also need to multiply
- the numerator by 2, so 1 times 2 is 2.
- And, of course, we still have this 3 out there.
- So 2 and 1/4 plus 1 and 5/8 is the same thing as this right
- here, and this is equal to-- we have our 3 plus, and then
- over 8 we add the 2 plus 5.
- We have 7/8.
- So this is going to be equal to 3 and 7/8 miles.
- She rode a total of 3 and 7/8 miles.
- Now, I want to make one thing very clear.
- So far when we've been adding these mixed numbers, the
- fraction part always ended up as a proper fraction.
- The numerator was smaller than the denominator.
- But I want to do a quick example to show you what you
- do when the numerator is not smaller than the denominator.
- So let's say we had 1 and 5/8 plus 2 and 4/8.
- So if you add just the whole number parts, 1
- plus 2, you get 3.
- Plus 5/8 plus 4/8, 5/8 plus 4/8 is 9/8, so
- you get 3 plus 9/8.
- Now it would be really strange to just say, OK, that's the
- same thing as 3 and 9/8, because you have a mixed
- number with a whole number and an improper fraction.
- If you're going through the trouble of making it a mixed
- number, the fraction better be a proper fraction.
- So what you need to do is rewrite 9/8, and you know that
- 9/8 is the same thing as 1 and 1/8, right?
- 8 goes into 9 one time with 1 left over, so it's 1 and 1/8.
- So this is the same thing as 3 plus 1 and 1/8.
- So now we can add the whole number parts.
- 3 plus 1 is equal to 4, and then you have your 1/8 over
- there: 4 and 1/8.
- I just wanted to give you that special circumstance when your
- fraction part ends up improper.