Simplifying Fractions
Sometimes when you see a fraction, it isn't in it's simplest form. For example, 8/12 isn't the simplest it can be. It can be simplified to 4/6 which can again be simplified to 2/3. To simplify the number, first we have to find the highest commmon factor of the denominator and the numerator. The highest common factor is simply the highest number that will divide into 2 other numbers and have a whole number as the result. For example the highest common factor of 12 and 8 is 4, as 4 is the highest number that divides into 12 (12/4 gives 3) and 8 (8/4 gives 2).
To find the highest common factor first you have to list all of the factors of the numbers. A factor of a number is simply any number which can be multiplied with another number to get the number you were trying to find factors of. For example the factors of 6 are 1, 2, 3 and 6, since all of them can multiply with another number to produce 6. Once you list down the factors of both numbers, find the common factors, the highest of these factors is the highest common factor. So for example, to find the highest common factor of 12 and 8, we find the factors of each. The factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 8 are 1, 2, 4, 8. The highest number which is common in these is 4.
Once you have found the highest common factor of the numerator and denominator, now you simply divide both numbers by the highest common factor, and you will now have the simplest form of the fraction. Lets apply this to a real fraction, for example, 15/20. The factors of 15 are 1, 3, 5 and 15, the factors of 20 are 1, 4, 5, 10, 20. The highest common factor in these is 5, so we divide both numbers by 5 to get 3/4. Now we still have the exact same fraction, only now it's in a simpler form.
Fractions Home Page
To find the highest common factor first you have to list all of the factors of the numbers. A factor of a number is simply any number which can be multiplied with another number to get the number you were trying to find factors of. For example the factors of 6 are 1, 2, 3 and 6, since all of them can multiply with another number to produce 6. Once you list down the factors of both numbers, find the common factors, the highest of these factors is the highest common factor. So for example, to find the highest common factor of 12 and 8, we find the factors of each. The factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 8 are 1, 2, 4, 8. The highest number which is common in these is 4.
Once you have found the highest common factor of the numerator and denominator, now you simply divide both numbers by the highest common factor, and you will now have the simplest form of the fraction. Lets apply this to a real fraction, for example, 15/20. The factors of 15 are 1, 3, 5 and 15, the factors of 20 are 1, 4, 5, 10, 20. The highest common factor in these is 5, so we divide both numbers by 5 to get 3/4. Now we still have the exact same fraction, only now it's in a simpler form.