ADDITION and SUBSTRACTION of Like FRACTIONS:
In order to add two or more like fractions, we may follow the two steps below:
- add or substract the numerators of all fractions;
and
- retain the common denominator of all fractions.
Example: Add or Substract the following like fractions
| ii) |
2
9
|
+ |
5
9
|
+ |
7
9
|
= |
14
9
|
| iii) |
2 |
3
5
|
+ |
4
5
|
+ |
1 |
2
5
|
= |
(2 × 5) + 3
5
|
+ |
4
5
|
+ |
(1 × 5) + 2
5
|
= |
24
5
|
| iv) |
1 |
1
4
|
+ |
2 |
3
4
|
+ |
7 |
1
4
|
= |
(1 + 2 + 7) |
1 + 3 + 1
4
|
= |
10 |
5
4
|
| v) |
8
10
|
− |
3
10
|
= |
5 1
10 2
|
(Dividing the numerator and denominator by their HCF = 5) |
= |
1
2
|
| vi) |
5
12
|
− |
7
12
|
+ |
11
12
|
= |
(5 − 7 + 11)
12
|
= |
9 3
12 4
|
(HCF = 3) |
= |
3
4
|
| vii) |
4 |
2
3
|
+ |
1
3
|
− |
4 |
1
3
|
= |
(4 × 3) + 2
3
|
+ |
1
3
|
− |
(4 × 3) + 1
3
|
= |
2
3
|
ADDITION and SUBSTRACTION of Unlike FRACTIONS:
To add or substract unlike fractions, we need to:
- firstly convert them into corresponding equivalent like fractions
by Finding the LCM of the denominators;
and
- secondly follow the same steps as in Like fractions
- add or sustract the numerators of all fractions;
and
- retain the common denominator of all fractions.
Example: Add or Substract the following unlike fractions
- To find the LCM of 3 and 7, we proceed to the following division:
- As you can see, 3 × 7 = 21 is the LCM of 3 and 7.
Since 21 can be divided by both 3 and 7: 21 ÷ 3 = 7 and 21 ÷ 7 = 3.
Now we can convert the given fractions into equivalent fractions with denominator 21 as follow:
|
2
3
|
+ |
3
7
|
= |
7 × 2
7 × 3
|
+ |
3 × 3
3 × 7
|
= |
14
21
|
+ |
9
21
|
= |
23
21
|
= |
1 |
2
21
|
- To find the LCM of 6 and 8, we proceed to the following division:
| 2 |
6, 8 |
| 2 |
3, 4 |
| 2 |
3, 2 |
| 3 |
3, 1 |
| |
1, 1 |
- As you can see, 2 × 2 × 2 × 3= 24 is the LCM of 6 and 8.
Since 24 can be divided by both 6 and 8: 24 ÷ 6 = 4 and 24 ÷ 8 = 3.
Now we can convert the given fractions into equivalent fractions with denominator 24 as follow:
|
1
6
|
+ |
3
8
|
= |
4 × 1
4 × 6
|
+ |
3 × 3
3 × 8
|
= |
4
24
|
+ |
9
24
|
= |
13
24
|
| iii) |
4 |
2
3
|
− |
3 |
1
4
|
+ |
2 |
1
6
|
= |
(4 × 3) +2
3
|
− |
(3 × 4) + 1
4
|
+ |
(2 × 6) + 1
6
|
|
= |
14
3
|
− |
13
4
|
+ |
13
6
|
Let's first find the LCM 0f 3, 4 and 6:
| 2 |
3, 4, 6 |
| 2 |
3, 2, 3 |
| 3 |
3, 1, 3 |
| |
1, 1, 1 |
|
As you can see, 2 × 2 × 3 = 12 is the LCM of 3, 4 and 6.
For, 12 can be divided by 3, 4 and 6: 12 ÷ 3 = 4, 12 ÷ 4 = 3 and 12 ÷ 6 = 2. |
Now let's convert the given fractions into equivalent fractions with denominator 12 as follow:
|
14
3
|
− |
13
4
|
+ |
13
6
|
= |
4 × 14
4 × 3
|
− |
3 × 13
3 × 4
|
+ |
2 × 13
2 × 6
|
= |
56
12
|
− |
39
12
|
+ |
26
12
|
| = |
43
12
|
= |
3 |
7
12
|
| iv) |
15
16
|
− |
17
24
|
, |
The LCM of 16 and 24 is: 2 × 2 × 2 × 2 × 3 = 48, |
(see table) |
| 2 |
8, 12 |
| 2 |
4, 6 |
| 3 |
2, 3 |
| 3 |
1, 3 |
|
1, 1 |
|
The fractions are now converted into equivalent fractions with like denominators, 48:
| ↔ |
15
16
|
− |
17
24
|
| = |
3 × 15
3 × 16
|
− |
2 × 17
2 × 24
|
| = |
45
48
|
− |
34
48
|
| = |
11
48
|
◄◄Fractions Core Lessons
|
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