What is the formula for finding equivalent fractions and reducing?

Answer 1

To find an equivalent fraction, you multiply your fraction (for example 5/10) by 1. For example: 8/8 equals 1, so if you multiply 5/10 x 8/8 (just multiply numerator x numerator and denominator x denominator), it equals 40/80, which is equivalent to 5/10 (or 1/2).

To reduce a fraction to simplest form, you must find the GCF of the numerator and denominator. The GCF stands for Greatest Common Factor. A factor is one of the numbers you multiply. For example: In the equation 3 x 5 = 15, 3 and 5 are the factors. So, let's use 5/10 as an example.

To list the factors of five, you must know your divisibility rules. Here are the basics, anyway. You have to go through every number until five. In other words, Can you divide 5 by one? Yes. 1 is a factor of 5. 1 is a factor of every number. Is 5 divisible by 2? No. 2 is not a factor of 5. Go through 3,4, and 5 the same way. Don't go to 6 because factors have nothing to do with negatives! Do the same thing with 10.

If you did it right these should be the factors of 5. 5 is prime, so you should've only gotten 1 and five.

10 is composite. That means it has more than 2 factors. 10's factors are 1,2, 5 and 10.

Now you find the GREATEST factor that these numbers have in COMMON. the only factors these numbers have in common are 1 and 5 and 5 is greater than 1.

Now you divide 5/10 by the GCF/GCF, which in this case would happen to be 5/5. Since 5/5 = 1, the fractions will have the same value.

Just divide the numerator of 5/10 by the GCF which is 5. 5 divided by 5 is 1. 1 is your new numerator.

Do the same for the denominator (10 divided by 5 is 2; 2 is your new denominator).

Your simplified fraction is now 1/2! 5/10 is equivalent to 1/2!

~Don't worry! It is not that complicated and can be confusing at first. Just practice and it will eventually become easy as pi (hidden nerd joke)! ;) Good luck!~