How can I solve fraction problems without a calculator?

[juniorb0y007]

I am taking college algebra this semester at my Community College. Prerequisite for pre-calculus . I have been doing good in math, but i have done fractions on calculator. I really don't know how to solve fractions (Addition & Subtractions) Problems without calculator.Please explain me how to deal with fractions without using calculators. It would be nice if you solve some problems.
Thanks
God Bless you

 

[rocomath]

Say we want to add ...

$$\frac a b + \frac c d$$

What we need is to get a common denominator. First we find it's LCD, which will be the product of "bd" by simply multiplying the missing variable to each term. Of course, when I say we multiply the term by the missing variable, we multiply both it's numerator and denominator by that variable. By multiplying both numerator and denominator by the same variable, it's an implied manipulation/multiplication of 1, which ensures our problem is unchanged.

$$\frac a b \cdot \frac d d + \frac c d \cdot \frac b b = \frac{ad}{bd}+\frac{cb}{db}$$

And since bd=db, I choose to write it as bd. Now they both have the same denominator! So you can write it under one denominator, and simply add the terms in the numerator.

$$\frac{ad+cb}{bd}$$

Still typing, keep refreshing.

Ok, now we'll use numbers.

$$\frac 1 2 + \frac 1 3$$

$$\frac 1 2 \cdot \frac 3 3 + \frac 1 3 \cdot \frac 2 2 = \frac{1\cdot 3}{2\cdot 3}+\frac{1\cdot 2}{2\cdot 3}=\frac 5 6$$

 

[Poop-Loops]

Some clarifications: LCD means "lowest common denominator".

An example:

1/7 + 3/5

What you is multiply 1/7 by 5/5. 5/5 = 1, so you're really not doing ANYTHING, just making it look different. The reason you are multiplying it by 5 is because the other fraction has a 5 on the bottom.

So 1/7 * 5/5 = 5/35

For the next fraction, we multiply it by 7/7, because again it = 1 and 7 is on bottom of the first fraction.

So 3/5 * 7/7 = 21/35

Now you can add 5/35 + 21/35 = 26/35

I've never used rocophysics's method, but try whichever one is easier for you.

Just remember that the goal is to get both fractions to have the same number on the bottom.

 

[rocomath]

I've never used rocophysics's method, but try whichever one is easier for you.

I don't see a difference in what we did? Lol

 

[tribalman100]

here ill try to help you

5''''''''''''3
---'''+''-----
8'''''''''''''5

Next Step: Get the same bottom part of the fraction or denominator
You Do this by Multiplying the bottom number in order to get the same number. In this case it is 40 since 8 goes into 40 5 times and 5 goes into 40 eight times

there fore

25'''''''''''''24
----'''+'''------
40'''''''''''''40

then you can add them up because same bottom so your answer is 49/40

 

[Gib Z]

Nothing we can teach you here will really be as beneficial as a good elementary algebra book. Search for them on amazon or something, they should be cheap as chips.

 

[mindCrime]

"Algebra Demystified" by Rhonda Huettenmueller is what I'm going through right now myself, as a refresher to help with my Pre-Calc class. It does a pretty good job of explaining this kind of stuff, and it's not very expensive. Might be worth a look if you want some extra material to help with the basics.

A quick point on LCDs... just multiplying the denominators will give you a number that will work, but it won't always be the *least* common denominator. For example if the fractions are:

$$\frac{1}{3}$$

$$\frac{ 1}{8}$$

$$\frac {1}{6}$$

the LCD is 24. The goal is to get the smallest number that all of the given denominators divide evenly into. Otherwise you wind up with larger numbers at the end and have more reducing to do then.

 

[arildno]

Do not bother with finding LCD's.

Just multiply the denominators together and find a suitable common denominator.