Say you have two fractions and you want to add them. How to go about this?
The question: 1/4 + 2/3
1. Look at the denominator, the number on the bottom of the fraction. These need to be the same number in order for a fraction to add. 4 and 3 aren't the same, so how to change the fraction so they are?
2. Find the Lowest Common Multiple. The LCM is the smallest (same) number that the 4 and 3 can make by multiplying. So, multiples of 4 are: 4, 8, 12, 16, 20... Multiples of 3 are 3, 6, 9, 12, 15... the first multiple that the 3 and 4 have in common is 12, so we have to change the denominator to 12.
3. Change the denominator by multiplying. Also, remember that since this is a fraction, what you do to the bottom, you have to do the same to the top to keep the ratio the same. So there's 1/4. You want to multiply the 4 by 3 to get 12. Do the same to the top, so 1x3 is 3. Final answer: 3/12. Now do the same to the 2/3. To get 12 on the bottom, you'll need to multiply the top and bottom by 4. So it becomes 8/12.
4. Now you have 3/12 + 8/12. The denominator is the same, so you can freely add the top numbers. 3+8= 11. The denominator stays the same. So the final answer is 11/12.
*Note: If you wanted to subtract fractions, you do exactly the same steps, except on step 4 you simply subtract the top two numbers instead of adding. So 3/12 - 8/12 would be -5/12 (negative because 3-8 is negative... if the equation was switched around to be 2/3 - 1/4, which then becomes 8/12 - 3/12, you would have 5/12 for an answer).
Multiplying and Dividing are a bit different.
Say you have 1/4 x 2/3
Don't care about the denominators, simply multiply straight across - so the top numbers multiply to become 1x2=2 and the bottom numbers: 4x3=12. So it's 2/12. Then you must reduce this number by dividing both by the Highest Common Factor. To find this, look at the numbers that make each number when you multiply them: to get 2, you can only multiple 1 with 2. To get 12, you can multiply 1 with 12, 2 with 6, and 3 with 4. The highest common factor is 2, so divide the top and bottom numbers (of 2/12) by 2: 2 divided by 2 = 1. 12 divided by 2 = 6. Answer: 1/6. Once you can no longer go any lower, you have your final answer.
Dividing has just one more step: you must flip one fraction over, and change the dividing sign to a multiplying sign. So if you start off with 1/4 divided by 2/3, it becomes 1/4 multiplied by 3/2. Then you simply multiply across: 1x3= 3, 4x2= 8, final answer: 3/8. This answer can't be reduced because the Higher Common Factor for 3 and 8 is 1, and dividing by 1 gives the same answer all the time.