## Introduction

In this lesson, we will talk about subtraction of fractions and mixed numbers. This is a very important topic because we use subtraction everyday and so it is important to review this with fractions and mixed numbers!

## Subtracting Fractions

Let's say that we have the problem 5/6-2/7

The first step is to find common denominators.

Remember that it is very important to have common denominators when adding or subtracting fractions and mixed numbers!

In order to find common denominators, we need to list the common multiples of each number and then find a common multiple. That common multiple will become your common denominator!

Multiples of 6:  6, 12, 18, 24, 30, 36, 42
Multiples of 7:  7, 14, 21, 28, 35, 42

As you can see, we have found a common multiple of 42.

-----   minus  -----
42                   42

Now that we have our common denominators, we need to find our numerators. We do that by dividing our common denominator by the previous denominator and then multiplying the quotient by the previous numerator to get our new numerator!

42/6= 7*5= 35
42/7= 6*2= 12

35                  12                23
-----  minus  -----  equals    -----
42                  42                 42

That means the difference between 5/6 and 2/7 equals 23/42!

## Subtracting Mixed Numbers

Let's say that we have the problem 3 2/3 minus 1 5/7

The first step is to convert the mixed numbers into improper fractions. In order to do that multiply the whole number by the denominator and then add the product to the numerator. The sum will become your numerator and the denominator will stay the same.

11/3 minus 12/7

The next step is to find a common denominator. We do that by finding a common multiple of the two denominators.

Multiples of 3: 3, 6, 9, 12, 15 ,18, 21
Multiples of 7: 7, 14, 21

As you can see we have found a common denominator of 21.

-----  minus  -----
21                  21

Now that we have our common denominators, we need to find our numerators. We do that by dividing our common denominator by the previous denominator and then multiplying the quotient by the previous numerator to get our new numerator!

21/3 = 7*11= 77
21/7=  3*12= 36

77                 36                 41
-----  minus  -----  equals  -----
21                 21                  21

Now the last step is converting our improper fraction answer into a mixed number. We can do that by dividing the numerator by the denominator:

41/21  equals 1 remainder  20.

Remember:

Quotient becomes Whole Number = 1
Remainder becomes Numerator  = 20
Divisor becomes Denominator  = 21

Put it all together and you get 1 20/21
That means the difference between 3 2/3 minus 1 5/7 equals 1 20/21!

Sheet 1 Subtracting Fractions and Mixed Numbers