0:00:01.121,0:00:05.038
Regina rode her bike 2 and 1/4[br]miles from her house to school

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and then 1 and 5/8 miles[br]to her friend's house.

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How many miles did Regina[br]ride in total?

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So she first rode 2 and 1/4[br]miles, and then she

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rode 1 and 5/8 miles.

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then she rode 1 and 5/8 miles

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So the sum is the total number[br]of miles she rode.

0:00:27.772,0:00:30.972
So to take this sum, we've seen[br]that we can add the whole

0:00:30.972,0:00:33.039
number parts, because this is[br]really the same thing as 2

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plus 1/4 plus 1 plus 5/8, so we[br]can just switch the order,

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if you want to view[br]it that way.

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So we can add the 2 plus the 1[br]first, and then we get-- let

0:00:42.572,0:00:43.489
me do that here.

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So 2 plus the 1, you get 3, and[br]then we need to add the

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1/4 plus 5/8.

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And to add these two fractions,[br]we have to find the

0:00:57.189,0:00:59.972
least common multiple[br]of 4 and 8.

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That'll be our new[br]denominator.

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8 is divisible by both 8 and 4,[br]so that is the least common

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multiple of 4 and 8, so our[br]common denominator will be 8.

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Obviously, 5/8 will[br]still be 5/8.

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Now to go from a denominator[br]of 4 to 8, you have to

0:01:24.154,0:01:26.572
multiply the denominator by 2,[br]so we also need to multiply

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the numerator by 2,[br]so 1 times 2 is 2.

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And, of course, we still[br]have this 3 out there.

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So 2 and 1/4 plus 1 and 5/8 is[br]the same thing as this right

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here, and this is equal to-- we[br]have our 3 plus, and then

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over 8 we add the 2 plus 5.

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We have 7/8.

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So this is going to be equal[br]to 3 and 7/8 miles.

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She rode a total of[br]3 and 7/8 miles.

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Now, I want to make one[br]thing very clear.

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So far when we've been adding[br]these mixed numbers, the

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fraction part always ended[br]up as a proper fraction.

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The numerator was smaller[br]than the denominator.

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But I want to do a quick example[br]to show you what you

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do when the numerator is not[br]smaller than the denominator.

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So let's say we had 1 and[br]5/8 plus 2 and 4/8.

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So if you add just the[br]whole number parts, 1

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plus 2, you get 3.

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Plus 5/8 plus 4/8, 5/8[br]plus 4/8 is 9/8, so

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you get 3 plus 9/8.

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Now it would be really strange[br]to just say, OK, that's the

0:02:40.555,0:02:43.271
same thing as 3 and 9/8, because[br]you have a mixed

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number with a whole number[br]and an improper fraction.

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If you're going through the[br]trouble of making it a mixed

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number, the fraction better[br]be a proper fraction.

0:02:50.604,0:02:53.239
So what you need to do is[br]rewrite 9/8, and you know that

0:02:53.239,0:02:59.521
9/8 is the same thing[br]as 1 and 1/8, right?

0:02:59.521,0:03:04.621
8 goes into 9 one time with 1[br]left over, so it's 1 and 1/8.

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So this is the same thing[br]as 3 plus 1 and 1/8.

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So now we can add the[br]whole number parts.

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3 plus 1 is equal to 4, and then[br]you have your 1/8 over

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there: 4 and 1/8.

0:03:16.554,0:03:18.805
I just wanted to give you that[br]special circumstance when your

0:03:18.805,9:59:59.000
fraction part ends[br]up improper.