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

In adding fractions, one must consider the type of fraction about to be added.

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

**Example:**

1/5 + 2/5 = 3/5

- 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.

- 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

- 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

We can now add:

21/12 + 34/12 = 55/12

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

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.

**Examples:**

7/8 – 1/8 = 6/8

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

**Examples:**

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.

In this process, the signs are also disregarded. We just multiply the numbers.

**Examples:**

- 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.

**Examples:**

- 1 5/8 – 3/8

= 1 2/8

= 1 1/4 - 6 3/6 – 2 1/6

= 4 2/6

= 4 1/3 - 8 2/7 – 7 1/7

= 1 1/7 - 10 2/3 – 1 1/3

= 9 1/3 - 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

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