To multiply fractions, all you have to do is multiply the numerators and denominators together and then simplify the result. To divide them, instead, you just have to flip one of the two fractions, multiply and finally simplify. If you want to learn how to do this in a flash, read on.
Steps
Method 1 of 2: Multiplication
Step 1. Multiply the numerators together
These are the numbers found at the top of the fraction, while the denominators are found under the fraction sign. The first step to multiply fractions with each other is to write them well aligned so that the numerators and denominators are close to each other. If you need to multiply 1/2 by 12/48, then first you need to multiply the numerators 1 and 12 together. 1 x 12 = 12. Write the product, 12, in place of the numerator of the solution.
Step 2. Multiply the denominators together
Now repeat the process for the denominators. Multiply 2 and 48 together to find the denominator of the solution. 2 x 48 = 96. Write the value in place of the denominator of the resulting fraction, which is: 12/96.
Step 3. Simplify the result
The last step is simplification, if possible. To do this, you need to find the greatest common divisor (GCD) of both the denominator and the numerator. The GCD is the largest number that can divide both the denominator and the numerator without leaving a remainder. In the case of 12 and 96 this value is 12. So proceed to divide 12 by 12 and you will get 1; then divide 96 by 12 and you will get 8. 12/96 ÷ 12/12 = 1/8.
If the numerator and denominator are even numbers, you can start dividing them by 2 and then continue. 12/96 ÷ 2/2 = 6/48 ÷ 2/2 = 3/24. At this point you realize that 24 is divisible by three so: 3/24 ÷ 3/3 = 1/8
Method 2 of 2: Division
Step 1. Flip the second fraction and change the division sign to the multiplication sign
Let's say you need to divide the fraction 1/2 by 18/20. At this point, swap the denominator and numerator of the second fraction, 18/20, and transform the division sign into the multiplication sign. So: 1/2 ÷ 18/20 = 1/2 x 20/18.
Step 2. Multiply the numerators together and do the same with the denominators, finally simplify the result
You will have to proceed as a normal multiplication. Considering the previous example, multiplying 1 and 20 you will get 20, transcribe this value in place of the numerator of the solution. Do the same with the denominators. Multiply 2 with 18 and you get 36 in the denominator. The product fraction is 20/36. 4 is the greatest common factor for the denominator and numerator, so divide both of them to simplify the solution: 20/36 ÷ 4/4 = 5/9.
Advice
- Always check your calculations twice.
- Remember that whole numbers can be written in the form of fractions. 2 is equivalent to 2/1.
- Don't forget to simplify.
- You can use cross-simplification at any time to save yourself some work. This method involves dividing diagonally by common factors. For example in multiplication (8/20) * (6/12) you can simplify up to (2/10) * (3/3).
- Always double check the work; if in doubt ask the teacher.
Warnings
- Do one step at a time. This way the chance of making mistakes will be minimal.
- There is always more than one way to solve math problems. However, just because once you get a correct result with a certain method doesn't mean that method will always work. Another method for dividing fractions is to do cross-multiplication, i.e. multiply diagonally.
- Remember to simplify it completely. An incomplete simplification can be considered as not having simplified at all.
