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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. |
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How to do add fractions |
| 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 |
For fractions with different denominators you have to:
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- Find the LCD (Least Common Denominator).
- Change the fractions to have the same LCD.
- Add the numerators.
- Reduce to lowest term.
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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: |
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- 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.
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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
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| For mixed fractions with different denominators, you have to:
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- 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.
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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
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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
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| For fractions with different denominators you have to:
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- Find the LCD (Least Common Denominator).
- Change the fractions to have the same LCD.
- Subtract the numerators.
- Reduce to the lowest term.
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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:
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- 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.
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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 |
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16 4/16
= 15 4/16 + 16/16
16 4/16
= 15 20/16 |
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15 20/16 – 7 5/16
= 8 15/16 |
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