How to Cancel Fractions

Canceling fractions is one of the few “legal” shortcuts in math. When you are multiplying or dividing fractions, you can make your work easier when you learn how to cancel in the problem. This may feel like cheating, but it is actually an acceptable thing to do in math and keeps you from having to reduce your answer. When you first learn to cancel fractions, you may find it a bit confusing. Stick with it, though, because canceling will make your life a whole lot easier when you get into more advanced types of math.

Instructions

Difficulty: Moderately Easy

Things You’ll Need:

• Paper
• Pencil

1. Copy the original problem down. Check to see if it is a multiplication or division problem.
2. Multiply by the inverse in a division problem. For instance, 3/4 divided by 1/2 would need to be changed to 3/4 times 2/1. Whenever you divide fractions, you always flip the second fraction and change the problem to multiplication.
3. Look at the numerators and denominators. Decide if there are any common factors, or numbers that you can evenly divide into both the numerator and denominator. For instance, in 3/4 times 2/1, the 2 and the 4 have a common factor of 2.
4. Divide the numerator and denominator you have chosen by the common factor. In the example, you will have 3/2 times 1/1. On your paper you will cross out the number you have and put the new number that you get when you divide by the common factor.
5. Multiply numerators together and multiply denominators together to get your answer. In this problem the answer is 3/2.
6. Reduce your answer or make it a mixed number if needed. In the example the answer would be 1 1/2. Proper canceling will make it so that you do not need to reduce your answer. However, you may need to make it into a mixed number.
7. Remember that you can cancel more than once. For example, if you are multiplying 25/32 times 24/30, you will get to cancel several times.
8. Start canceling by dividing the 32 and the 24 by 8. This will give you 25/4 times 3/30. Then divide the 25 and the 30 by 5, giving you 5/4 times 3/6.
9. Divide the 3 and 6 by 3. It does not matter that these digits are found in the same fraction. This will give you 5/4 times 1/2. You cannot cancel the 4 and the 2 because they are both denominators.
10. Multiply and reduce or simplify your answer. The answer is 5/8, which cannot be simplified.

Tips & Warnings

• Remember that canceling will make it easier to multiply because you will be dealing with smaller numbers.
• Always simplify your answer, unless your teacher tells you not to do so.
• Never cancel in a division problem before you change it into a multiplication problem with the inverse of the second fraction.
• Never cancel a denominator and another denominator. You can only cancel by dividing by a common factor between a numerator and a denominator.