Question

I'm in a basic algebra class & need help with simplifying this equation: 15 over 24 + 3 over 24. Think the answer is one half but how do I get there step by step?

Answer 1

Do you mean:
\[\Large \frac{{15}}{{24}} + \frac{3}{{24}}\]
Because that's 18/24 = 3/4 not 1/2.

Answer 2

15 + 3/24
= 18/24
= 3/4

Answer 3

Yes this is what I meant. How did you get the answer?

Answer 4

Add 15 with 3 because the denominator is common. Then simplify 18/24 to get 3/4.

Answer 5

Because the denominators (the bottom part) are the same, you can simply add the numerators and get the one fraction; 15+3 = 18 so it becomes 18/24, divide both top and bottom by 6 (a common factor) and you get 3/4.

Answer 6

Maybe this will help:
\[\Large \begin{array}{l}
\frac{{15}}{{24}} + \frac{3}{{24}} = \frac{{15 + 3}}{{24}} = \frac{{18}}{{24}}\\
18 \div 6 = 3\\
24 \div 6 = 4\\
\frac{{18}}{{24}} = \frac{3}{4}
\end{array}\]

Answer 7

Ok this is very helpful. Now how do I find out that 6 is a common factor?

Answer 8

For larger numbers, there are a couple of tricks you can use; but for smaller numbers such as 18 and 24, and it's really just a matter of "knowing" which comes from practise and playing with numbers a lot.
While practising, you can write out all the factors of both numbers and see if any match (i.e. all numbers the number can be evenly divided by producing a whole integer):
24: 24, 12, 8, 6, 4, 3, 2, 1.
18: 18, 9, 6, 3, 2, 1.
Here, the highest common factor is 6, so you know to use that one.
For other numbers which you don't inherently know the factors of, it's generally easiest to use prime factorisation.

Answer 9

Understood. When you say that 6 is a common factor, does that also mean greatest common factor? If so, how can this be done with larger numbers?

Answer 10

What I need is a short method of doing this that will give the same results for the numbers.

Answer 11

Yeah sorry for the ambiguity, the greatest common factor is what you want to aim for. A common factor isn't necessarily the greatest common factor - 3, 2 and 1 are all common factors of 24 and 18 too - but it's the greatest (or highest) common factor you use here.

Answer 12

Can't thank you enough, meant to say need the shorter method for LARGER numbers...