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Addition and subtraction of fraction is shown in this topic. Fractions are numbers that represent a part of a whole. It contains two numbers; i.e. the numerator that is placed above the denominator.
 Numerator/denominator

### How to do add fractions

For fractions with the same denominator, just add the numerator and copy the denominator.

### Example:

1/5 + 2/5 = 3/5

For fractions with different denominators you have to:

 Find the LCD (Least Common Denominator). Change the fractions to have the same LCD. Add the numerators. Reduce to lowest term.

### Example:

2/4 + 4/18
Find the Greatest Common Factor (GCF) of 4 and 18 which is 2.
Multiply the denominators and divide it with the GCF.
4*18 = 72, 72/2 =36
So, our LCD is 36.
Next, change the fractions to the same denominator using the LCD.

36/4=9, 9*2=18

2/4=18/36

36/18=2, 2*4=8

4/18= 8/36

We can now add the fractions:

18/36 + 8/36 = 26/36

The answer could be further reduced to its lowest term by dividing the number by 2. The resulting fraction is 13/18.

For mixed fractions with the same denominator you have to:
 Add the fractions first. If the resulting fraction is improper (the numerator is equal to or bigger than the denominator), convert the fraction into a mixed fraction. Then, add the integers.

### Example:

3  4/9 + 4  6/9

4/9 + 6/9 = 10/9

10/9 = 1  1/9

3 + 4 + 1 = 8

So, the answer would be 8  1/9

For mixed fractions with different denominators, you have to:

 Change the mixed fraction into an improper fraction. Find the LCD (Least Common Denominator). Change the fractions to have the same LCD. Add the numerators. Reduce to the lowest term.

### Example:

1  3/4 + 2  5/6

Changing the mixed fractions above into improper fractions would result to:
1  ¾ = 7/4

2  5/6 = 17/6
We can now find the GCF of 4 and 6 which is 2.

Based on what we learned earlier our LCD would be:

4*6 = 24, 24/2 = 12

We can now change the fraction into the same LCD:

12/4 = 3, 3*7 = 21

7/4 = 21/12

12/6 = 2, 2*17 = 34

17/6 = 34/12

21/12 + 34/12 = 55/12

We then convert it back to mixed fraction and reduce it to its lowest term 4  7/12

### How to subtract fractions

In subtracting fractions, again one must consider the type of fraction you are about to subtract.
For fractions with the same denominator, just subtract the numerator and copy the denominator.

### Example:

7/8 – 1/8 = 6/8

For fractions with different denominators you have to:

 Find the LCD (Least Common Denominator). Change the fractions to have the same LCD. Subtract the numerators. Reduce to the lowest term.

### Example:

5/20 – 3/16
Find the Greatest Common Factor (GCF) of 20 and 16 which is 4.
Multiply the denominators and divide it with the GCF.
20*16=320, 320/4
So, our LCD is 80.

Next, change the fractions to the same denominator using the LCD.

80/20=4, 4*5=20

5/20=20/80

80/16=5, 5*3=15

3/16= 15/80

We can now subtract the fractions:

20/80 - 15/80 = 5/80

The answer could be further reduced to its lowest terms by dividing the numerator and the denominator with 5. The resulting fraction is 1/16.

For mixed fractions with the same denominator you have to:

 Look at the fractions that you are about to subtract. If the first numerator is smaller than the second, make the first numerator bigger than the second. Then, find the difference between the numerators and place it over the common denominator. You can now find the difference between the integers. Simplify the resulting fraction by reducing it to its lowest term.

### Example:

 1. 1  5/8 – 3/8 = 1  2/8 = 1  1/4 2. 6  3/6 – 2  1/6 = 4  2/6 = 4  1/3 3. 8  2/7 – 7  1/7 = 1  1/7 4. 10  2/3 – 1  1/3 = 9  1/3 5. 16  4/16 – 7  5/16 16  4/16 = 15  4/16 + 16/16 16  4/16 = 15  20/16 15  20/16 – 7  5/16 = 8  15/16