# Subtracting Fractions

### How to subtract mixed, improper, and proper fractions.

## Subtracting Mixed Fractions

To subtract mixed fractions, you need to change the mixed fraction to a improper fraction. To change a mixed fraction to a improper fraction you multiply the denominator by the whole number, and then you add the numerator. The answer you get will be the numerator over the denominator of the mixed fraction. Then you find a common denominator, once you find it you see how many times the denominators is multiplied to get that number. Then whatever you multiply at the bottom you do to the top too. You then multiply the numerator by the number, and then you get the answer over the common denominator. Then you subtract the numerators, that answer would be over the common denominator. Then you change the improper fraction to a mixed fraction, so you see how many times the denominator can go into the numerator. That would be the whole number, then the left over is the numerator over the common denominator.

## Example Of Subtracting Mixed Fractions

For this example, the equations is 4 and 2 over 3 subtract 2 and 1 over 4. First you change both the mixed fraction into a improper fraction. So you multiply the denominator by the whole number, then add the numerator. So 3x4 equals 12 then add 2, which equals 14 over 3. Then 4x2 equals 8 then add 1, which equals 9 over 4. Then you find the common denominator, in this case it would be 12 because 4x3 equals 12. Since you multiply the denominator of 3 by 4 you have to do it for the top too. So 14x4 equals 56 over 12, and do the same for the other fraction. So the denominator of 4 multiplied by 3, then you do the same for the top. So 9x3 equals 27 over 12. Then you subtract the numerators, so 56-27 equals 29. Since the denominators are the same it would be the same too. So the answer is 29 over 12, but you need to change it to a mixed fraction. So you see how many times 12 goes into 29, so that would be 2 times, so 2 is the whole number. Now the left overs are the numerator, so 5 is the left over. So the answer would be 2 and 5 over 12.

Subtracting mixed numbers

## Subtracting Improper Fractions

To subtract improper fractions you need to find the common denominator, once you find it, you see how many times the denominators is multiplied to get that number. Then whatever you multiply at the bottom you do to the top too. You then multiply the numerator by the number, and then you get the answer over the common denominator. Then you subtract the numerators, that answer would be over the common denominator. Then you change the improper fraction to a mixed fraction, so you see how many times the denominator can go into the numerator. That would be the whole number, then the left over is the numerator over the common denominator.

## Example Of Subtracting Improper Fractions

For this example, the equation is 17 over 8 subtract 13 over 12. First you need to find a common denominator, in this case it would be 24, because 8x3 equals 24, and 12x2 equals 24 too. Since you multiply the denominator of 8 by 3 you have to do the same for the top. So 17x3 equals 51 over 24, and do the same for the other fraction. So 13x2 equals 26 over 24. Then you subtract the numerators, so 51-26 equals 25 over 24. The denominator would stay the same because the fractions have the same denominator. Then you change the improper fraction to a mixed fraction. So you see how many times 24 goes into 25, so it would be 1 time. So 1 would be the whole number, and the left overs are the numerator. So 1 would be the numerator, and the denominator stays the same. So the answer would be 1 and 1 over 24.

Example: Subtract Mixed Numbers Using Improper Fractions

## Subtracting Proper Fractions

To subtract proper fractions you need to find the common denominator, once you find it, you see how many times the denominators is multiplied to get that number. Then whatever you multiply at the bottom you do to the top too. You then multiply the numerator by the number, and then you get the answer over the common denominator. Then you subtract the numerators, then that answer would be over the common denominator. Sometimes the fraction could be reduced to the lowest term, so you have to check if it can too.

## Example Of Subtracting Proper Fractions

For this example, the equation is 7 over 8 subtract 5 over 16. First we need to find a common denominator, in this case it would be 16, because 8x2 equals 16, and the second fraction has a denominator of 16. Since the second fraction has a denominator of 16 you will leave it alone. But since you multiply the denominator of 8 by 2 you have to do the same for the top. So 7x2 equals 14 over 16. Then you subtract the numerators, so 14-5 equals 9 over 16. Then I would check if 9 over 16 could be reduced to lowest term, but in this case it is already in the lowest term.

Subtracting Proper Fractions with Unlike Denominators