Adding Mixed Fractions and Estimation

Valerie said:

hi all need adding mixed fractions please.

and:

Hi curtis its valerie in florida again new question wow took the tape test and im ready to do the GED in Reading wow ok in math the total score was 5.0 G.E that she said had to get to 10.0 right ok she said to start in Estimation what is this rounding off ? please tell me what to do where to go in the ged study video ty.

Hey there, Valerie! First off, congrats on bein’ down with the reading. That’s one more done! Now, the math…

Estimating

Estimation is rounding off, like you said. But it’s also part of what I call mental math. In the passGED study program, you can go to the first math course (Learning about Numbers), and go to Unit 1, Lesson 6, to learn all about it. I call it mental math. You can estimate to make your job on the GED a lot easier, so you don’t have to do so much math. That means, goin’ through a problem an’ figuring out about what the numbers are, in round numbers that’re easy to work with. With multiple choice answers, if you figure out about what the right answer is, you save a lot of time. You don’t have to get it exact.

Say, I got a problem:

5,890 + 8,799 + 2,014 + 9,882 + 4,649

Okay, that’s gonna take a little time to work out on paper, but I also got some multiple choice answers:

A) 35,892

B) 31,234

C) 29,449

Can I figure it out without goin’ through all the math? Prolly. Here I go…

5,890 is about 6,000, and 8,799 is about 9,000, and 2,014 is about 2,000, and 9,882 is about 10,000, and 4,649 is about 4,500… so the question is ABOUT

6,000 + 9,000 + 2,000 + 10,000 + 4,500 which is ABOUT

6 + 9 + 2 + 10 + 4-1/2 thousand.

That’s like 6 + 9, is 15, plus 2 is 17, plus 10 is 27, plus 4-1/2 is 31-1/2…

So, it’s about 31,500. That’s pretty close to answer B. So that’s my choice. If you figure it out on a calculator, that’s it. See how good that can be savin’ you time on a test?

Adding Mixed Fractions

Fraction Basics…

Befo’ starting about fractions, here’s the link  to all my articles on fractions… http://www.passged.com/student_blogs/curtis/category/fractions/

You gotta start by really lookin’ at what a fraction is… I mean, you got two numbers in a fraction, right? One on top an’ one on the bottom. Like, 1/2… that’s an easy one to think about. The top number (1) is called the numerator, and the bottom number (2) is called the denominator. But that’s not the point. Remembering what they’z called is jus’ to help you understand what math books is talking about. What’s really important is what they mean. Think about a pizza. It’s divided in half. Each half is 1/2, right? That’s basic. The top number (1) is really the number of parts you have, and the bottom number (2) is the number of equal parts the whole thing is divided into. That make sense? So you got 1 part out of 2 parts… then, you got half.

Same thing if you got 3/4… say you got 3/4 of a box of candy. That means, if you divide the box into 4 equal parts, you got three of them. What happened to the other 1/4? Who knows? Maybe someone ate it.

So, if the whole box of candy originally had 16 chocolates in it, and you got 3/4 of the box, how many chocolates you got?

Now, there’s a GED math question for you… this is also called a ‘ratio,’ but really if you understand what fractions are, it’s pretty easy.

Say you got 16 chocolates, and you wanna divide it into 4 parts (see, 3/4 means its divided into 4 parts, right?) Then, you divide 16 by 4, and you get 4. See, 4 piles of 4 chocolates each is 16 all together… and each pile of 4 is 1/4 of all the chocolates. Hey, get 16 chocolates (or paperclips or anything) and give it a try. No way to learn like actually seeing it, right?

So if you got 3/4 of the chocolates, then you got 3 of the 4 piles. So, you multiply the number of chocolates in 1 pile (4) by the number of piles you got (3) to get the total number of chocolates you got… 12. D’you follow? Here it is in math terms:

How much is 3/4 of 16? (Of usually means multiply, so…)

3/4 x 16 = 3 x (16 ÷ 4) = 3 x 4 = 12

So, if 2/6 of the 24 people in your office vote to have hamburgers for lunch, how many people voted to have hamburgers for lunch?

2/6 x 24 = 2 x (24 ÷ 6) = 2 x 4 = 8

See how it works? If you divide 24 people into 6 equal groups, there are 4 people in each group. An’ if 2 groups vote for hamburgers, that’s 8 people.

Now on to the real question…

Adding Mixed Fractions

Mixed fractions is when you got a whole number like 3 plus a fraction like 3/4. So, if you’re addin’ mixed fractions you got something like this:

1-4/5 + 6-2/3

Problem is, it’s hard to add two fractions that have different bottom numbers. It’s like I was sayin’, if you have one set divided into 5 equal groups, and another set of things divided into 3 different groups, the groups will be different sizes. So, it’s like apples and oranges. You can’t add ‘em together.

So, you gotta figure out the smallest number that can go at the bottom of the fraction to make both fractions have the same bottom number. Well, a lot of the time, that number is the two denominators (bottom numbers) multiplied together. And that’s the case here. You can change both fraction to something-15ths.

4/5 = ?/15

This is jus’ like I was talking about before. Say you got a box of 30 chocolates, divided into 5 groups. Then, you got 6 chocolates in each group, right? And 4/5 of the chocolates would be 24 chocolates. (4 groups of 6 chocolates).

Now, what if you divide the chocolates into 15 groups? How many groups make up 24 chocolates? Well, if you divide 30 chocolates into 15 groups, you got 2 chocolates in each group. And 12 groups makes up 24 chocolates… 12 groups of 15 is the same as 4 groups of 5.

4/5 = 12/15

There’s a shortcut way to figure it out… because 5 x 3 is 15, you multiply the top number by the same thing (3) to get 12 on top. This always works! So…

2/3 = ?/15
since 3 x 5 = 15…
2/3 = (2 x 5)/15 = 10/15

Okay, now you got your numbers the same at the bottom….

1-4/5 + 6-2/3 = 1-12/15 + 6-10/15

Next step is to add the whole numbers and add the fractions. When you add fractions, just add the top numbers (12 groups plus 10 groups is 22 groups, no matter how big the groups are, right?)

1-4/5 + 6-2/3 = 1-12/15 + 6-10/15 = 7-22/15

Now, 22/15? If the top number’s bigger, then you got more than one. 15/15 is a complete set of groups… so it’s 1. That means, 22/15 = 1-7/15. So…

1-4/5 + 6-2/3 = 1-12/15 + 6-10/15 = 7-22/15 = 8-7/15

Hope this helps!