Reduce the fraction 28/132 to its simplest form

Answer 1

You must find a common factor shared by the numerator and the denominator. Factors are numbers you can multiply together to get another number. Factors are either composite numbers or prime numbers (except that 0 and 1 are neither prime nor composite).

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.

So, you may either find common factors (either prime, like 2, or composite, like 4) and divide both the numerator and the denominator by that factor, and keep doing that until you can't find any more common factors --- or, you could find all of the prime factors of each number when you start.

Prime factors of 28 = 2*2*7

Prime factors of 132 = 2*2*3*11

[Note that when a prime number occurs multiple times, an exponent may be used to show that.]

For this problem, (2*2) is a common factor. Cancel that in the numerator and the denominator. That leaves (7) / (3*11).

The simplest form is 7/33.

Now, if you learn a method for quickly finding prime factors of a composite number, this method is quick and it reduces the fraction completely [no more guesswork !].

Answer 2

One quick and easy answer, and one really hard to understand answer. And while helpful, they aren't teaching you how to approach reducing fractions. This example just happened to involve numbers that are divisible by two, but what should you do if that is not so obvious? The solution involves factors.

Factors of a number are the numbers, that when multiplied together, get that number. For instance, the factors of 6 are 1, 2, 3, 6 (1x6 = 6, 2x3=6). When reducing a fraction, you must first list the factors of the numerator and the denominator, then find the highest value shared by both. This value can then be used to reduce the fraction to it's smallest value. Finding the factors of a number can be difficult, especially when the numbers involved are large. 28 and 132 aren't terribly large, but 132 is large enough.

The first one is easy - every number times 1 is that number, so 1 a factor.

1x28

1x132

We then go up, testing the next value. The result must be a number, no remainder is allowed. But as we go up, the number being multiplied comes down (eventually, they should cross in the middle, and you can stop).

1x28 2x14 3x? 4x7 5x? 6x? done!

1x132 2x66 3x44 4x33 5x? 6x22 7x? ... we can stop there, as the number being tested is now higher than the factors we found for 28.

In comparing the two lists, we can see that the highest number that they both share is 4. This means that we can divided both the numerator and denominator by 4 (whatever you do to one, you must do to the other!).

This leaves you the result of 7/33, same as shown above.

Answer 3

What are 28 and 132 both divisible by?

They are both even, so they are divisible by 2.

14/66

Hey, those are both even, as well, so let's try 2 again.

7/33

Hopefully you know that 7 is a prime number, so we are done. Even though we can divide 33 by 3 or 11, neither divides into 7, so we are done.

28/132 = 7/33

Answer 4

28/132 = 7* 2²/(2²*11*3) = 7/33