CLASS-6
CONVERSION OF GIVEN FRACTION INTO LIKE FRACTION
CONVERSION OF GIVEN FRACTION INTO LIKE FRACTION -
To convert fractions into like fractions, you need to make sure that the denominators of the fractions are the same. Once the denominators are the same, you can compare and perform operations with the numerators directly. Here's how you can do it:
Step 1:- Find the least common multiple (LCM) of the denominators of the fractions.
Step 2:- Use the LCM as the new common denominator for both fractions.
Step 3:- Convert the fractions to equivalent fractions with the new common denominator.
Let's illustrate with an example.
Example.1) Convert 2/3 and 1/4 into like fractions.
Step 1:- Find the LCM of 3 and 4. The multiples of 3 are: 3, 6, 9, 12, 15, ... The multiples of 4 are: 4, 8, 12, 16, 20, ... The LCM of 3 and 4 is 12.
Step 2:- Use 12 as the common denominator.
Step 3:- Convert the fractions to equivalent fractions with a denominator of 12.
For 2/3: Multiply both the numerator and denominator by (12/3) to get the equivalent fraction: (2/3) * (12/3) = 24/36
For 1/4: Multiply both the numerator and denominator by (12/4) to get the equivalent fraction: (1/4) * (12/4) = 12/36
Now, both fractions are expressed with the common denominator of 36.
So, the like fractions are: 2/3 = 24/36 1/4 = 12/36
3 5 7
Example.2) Convert -----, ------, and ------ into like fractions.
4 6 8
Ans.)
Step 1:- Find the LCM of 4, 6, and 8.
The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
The multiples of 6 are: 6, 12, 18, 24, ...
The multiples of 8 are: 8, 16, 24, ...
The LCM of 4, 6, and 8 is 24.
Step 2:- Use 24 as the common denominator. So,
(i) divide 24 by denominator 4 of first given fraction and obtain 6 and now multiply both denominator and numerator of first given fraction by 6.
(ii) divide 24 by denominator 6 of second given fraction and obtain 4 and now multiply both denominator and numerator of second given fraction by 4.
(iii) divide 24 by denominator 8 of third given fraction and obtain 3 and now multiply both denominator and numerator of third given fraction by 3.
Step 3:- Convert the fractions to equivalent fractions with a denominator of 24.
3 3 X 6 18
------ = --------- = -------
4 4 X 6 24
5 5 X 4 20
------ = ---------- = --------
6 6 X 4 24
7 7 X 3 21
------ = ---------- = --------
8 8 X 3 24
So, the equivalent like fractions are -
3 5 7 18 20 21
------ = ------ = ------ => ------- = ------- = -------
4 6 8 24 24 24
3 5 7
Example.3) Convert 1 -----, 2 -----, and 3 ----- into like fractions.
4 6 8
Ans.)
Step.1) First convert all the given mix fraction into improper fraction.
3 (1 X 4) + 3 4 + 3 7
1 ------ = -------------- = --------- = ------
4 4 4 4
5 (2 X 6) + 5 12 + 5 17
2 ------ = ------------- = ---------- = ------
6 6 6 6
7 (3 X 8) + 7 24 + 7 31
3 ------ = ------------- = ---------- = -------
8 8 8 8
Step.2) Find the LCM of 4, 6, and 8.
The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
The multiples of 6 are: 6, 12, 18, 24, ...
The multiples of 8 are: 8, 16, 24, ...
The LCM of 4, 6, and 8 is 24.
Step.3) Use 24 as the common denominator. So,
(i) divide 24 by denominator 4 of first given fraction and obtain 6 and now multiply both denominator and numerator of first given fraction by 6.
(ii) divide 24 by denominator 6 of second given fraction and obtain 4 and now multiply both denominator and numerator of second given fraction by 4.
(iii) divide 24 by denominator 8 of third given fraction and obtain 3 and now multiply both denominator and numerator of third given fraction by 3.
Step.4) Convert the fractions to equivalent fractions with a denominator of 24.
Now, we would like to convert from improper fraction to equivalent fraction.
7 7 X 6 42
------- = ---------- = -------
4 4 X 6 24
17 17 X 4 68
------- = ---------- = --------
6 6 X 4 24
31 31 X 3 93
------- = ---------- = --------
8 8 X 3 24