GED Math: Adding and Subtracting Fractions

Hey, all. Michael’s studyin’ for his GED, an he sent me this question:

am having problem with Lesson-7 page 491 on A. on Add or subtract as Directed reduce to the lowest terms.Am trying to figure out the form to work the fractions. am stuck on this one. Michael

Okay, here’s the rule with adding and subtracting fractions. Let’s start with a problem:

5/12 + 2/5

For starters, make sure you got the same number on the bottom of both fractions (the same denominator). If the denominators are different (like 12 and 5), how do you get them the same?

Well, you can change the number on the bottom of a fraction by multiplying or dividing BOTH the number at the top (numerator) and the number at the bottom (denominator) by the same number. So, what’s a number you can multiply 12 and 5 into evenly? Gotta go all the way up to 60 to do it. I figure it out by seeing what the multiples of 12 are, until I find one that 5 goes into (cuz I know 5 will go into it if it ends in 5 or 0). Hey, practice those times tables!

So, since 12 x 5 is 60, you change the denominator of the first fraction to 60 by multiplying the top and bottom by 5:

5/12 = (5 x 5) / (12 x 5) = 25/60

For the second fraction, you gotta multiply by 12:

2/5 = (2 x 12) / (5 x 12) = 24/60

So, the problem gets to be:

25/60 + 24/60 =

Now, it’s easy. Just add the top numbers, and the bottom number stays the same:

25/60 + 24/60 = 49/60

Now, you want to REDUCE. That means, is there anything you can divide evenly into the top and bottom? No, there isn’t. So the answer is 49/60. Let’s try a subtraction problem… they’re similar. Make the bottom numbers the same, and then subtract the top numbers. But let’s mix it up with mixed numbers.

5-1/4 – 3-2/3 =

Okay, there are a couple of ways to do this, but I find the easiest is to make them into improper fractions first. How many 4ths is 5? It’s 20/4 (4 x 5 = 20). So, 5-1/4 = 21/4… you can do the same thing with 3-2/3. Three is the same as 9/3 (or 3 x 3 thirds), so 3-2/3 = 11/3 (9 thirds plus 2 thirds is 11 thirds). Now, it’s just fractions:

21/4 – 11/3 =

So, how do we make 4 and 3 the same? What do they both go into? 12.

21/4 = (21 x 3) / (4 x 3) = 63/12

11/3 = (11 x 4) / (3 x 4) = 44/12

To figure out the problem, just subtract the top numbers, and leave the bottom one the same:

63/12 – 44/12 = (63 – 44)/12 = 19/12

Now, what’s 19/12? Take 12/12 out to make 1, and you’ve got 7/12 left: 1-7/12.

Okay, we didn’t really reduce on any of these, so let’s do one that needs to reduce.

11/36 + 7/36 =

The bottom numbers are already the same, so just add the top numbers and leave the bottom number the same:

11/36 + 7/36 = (11 + 7)/36 = 18/36

Okay, now we got 18/36. It needs to be reduced. How do I know? Well, first they’re both even numbers, so I know for sure that 2 goes into both. (If they both ended in either 0 or 5, I’d know 5 went into both… seriously, check your times tables.)

Since 2 goes into both, I can divide both by 2:

18/36 = (18 ÷ 2) / (36 ÷ 2) = 9/18

Now, I can see pretty clear that 9 goes into 18:

9/18 = (9 ÷ 9) / (18 ÷ 9) = 1/2

So, 18/36 is 1/2. If I saw right away that 36 was twice 18, I wouldn’t'a had to divide twice… that’s why it helps your GED to get really good at the basic math, dividing, multiplyin’, just workin’ with numbers.

Let me know if this helps studyin’ for your GED! And let me know if you got any more questions abou adding and subtracting fractions.

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.