How To Add Fractions Algebra

regina rode her bike 2 and 1/4miles from her house to school and then 1 and 5/8 milesto her friend's house. how many miles did reginaride in total? so she first rode 2 and 1/4miles, and then she rode 1 and 5/8 miles.

How To Add Fractions Algebra, so the sum is the total numberof miles she rode. so to take this sum, we've seenthat we can add the whole number parts, because this isreally the same thing as 2 plus 1/4 plus 1 plus 5/8, so wecan just switch the order,

if you want to viewit that way. so we can add the 2 plus the 1first, and then we get-- let me do that here. so 2 plus the 1, you get 3, andthen we need to add the 1/4 plus 5/8. and to add these two fractions,we have to find the least common multipleof 4 and 8. that'll be our newdenominator. 8 is divisible by both 8 and 4,so that is the least common

multiple of 4 and 8, so ourcommon denominator will be 8. obviously, 5/8 willstill be 5/8. now to go from a denominatorof 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 stillhave this 3 out there. so 2 and 1/4 plus 1 and 5/8 isthe same thing as this right here, and this is equal to-- wehave our 3 plus, and then over 8 we add the 2 plus 5.

we have 7/8. so this is going to be equalto 3 and 7/8 miles. she rode a total of3 and 7/8 miles. now, i want to make onething very clear. so far when we've been addingthese mixed numbers, the fraction part always endedup as a proper fraction. the numerator was smallerthan the denominator. but i want to do a quick exampleto show you what you do when the numerator is notsmaller than the denominator.

so let's say we had 1 and5/8 plus 2 and 4/8. so if you add just thewhole number parts, 1 plus 2, you get 3. plus 5/8 plus 4/8, 5/8plus 4/8 is 9/8, so you get 3 plus 9/8. now it would be really strangeto just say, ok, that's the same thing as 3 and 9/8, becauseyou have a mixed number with a whole numberand an improper fraction. if you're going through thetrouble of making it a mixed

number, the fraction betterbe a proper fraction. so what you need to do isrewrite 9/8, and you know that 9/8 is the same thingas 1 and 1/8, right? 8 goes into 9 one time with 1left over, so it's 1 and 1/8. so this is the same thingas 3 plus 1 and 1/8. so now we can add thewhole number parts. 3 plus 1 is equal to 4, and thenyou have your 1/8 over there: 4 and 1/8. i just wanted to give you thatspecial circumstance when your

fraction part endsup improper.