To compare fractions with different denominators, we have to follow the steps given below.
Step 1 :
Find the least common multiple of denominators and make the denominators same.
Step 2 :
Now by comparing the numerators and decide which numerator greater that will be greater fraction.
Compare the fractions. Write <,>, or =.
Problem 1:
Solution :
In the fractions 3/4 and 3/8, the denominators are different.
LCM of (4, 8) = 8
3/4 = (3 ∙ 2) / (4 ∙ 2) ==> 6/8
3/8 = (3 ∙ 1) / (8 ∙ 1) = 3/8
Compare the numerators of like fractions 6/8 and 3/8.
6/8 > 3/8
Substitute the corresponding original fractions.
3/4 > 3/8
Problem 2 :
Solution :
In the fractions 2/3 and 4/5, the denominators are different.
LCM of (3, 5) = 15
2/3 = (2 ∙ 5) / (3 ∙ 5) = 10/15
4/5 = (4 ∙ 3) / (5 ∙ 3) = 12/15
Compare the numerators of like fractions 10/15 and 12/15.
10/15 < 12/15
Substitute the corresponding original fractions.
2/3 < 4/5
Problem 3 :
Solution :
In the fractions 1/5 and 2/10, the denominators are different.
LCM of (5, 10) = 10
1/5 = (1 ∙ 2) / (5 ∙ 2) = 2/10
2/10 = (2 ∙ 1) / (10 ∙ 1) = 2/10
Compare the numerators of like fractions 2/10 and 2/10.
2/10 = 2/10
Substitute the corresponding original fractions.
1/5 = 2/10
Problem 4 :
Solution :
In the fractions 2/10 and 23/100, the denominators are different.
LCM of (10, 100) = 100
2/10 = (2 ∙ 10) / (10 ∙ 10) = 20/100
23/100 = (23 ∙ 1) / (100 ∙ 1) = 23/100
Compare the numerators of like fractions 20/100 and 23/100.
20/100 < 23/100
Substitute the corresponding original fractions.
2/10 < 23/100
Problem 5 :
Solution :
In the fractions 7/8 and 3/4, the denominators are different.
LCM of (8, 4) = 8
7/8 = (7 ∙ 1) / (8 ∙ 1) = 7/8
3/4 = (3 ∙ 2) / (4 ∙ 2) = 6/8
Compare the numerators of like fractions 7/8 and 6/8.
7/8 > 6/8
Substitute the corresponding original fractions.
7/8 > 3/4
Problem 6:
Solution :
In the fractions 7/12 and 5/6, the denominators are different.
LCM of (12, 6) = 12
7/12 = (7 ∙ 1) / (12 ∙ 1) = 7/12
5/6 = (5 ∙ 2) / (6 ∙ 2) = 10/12
Compare the numerators of like fractions 7/12 and 10/12.
7/12 < 10/12
Substitute the corresponding original fractions.
7/12 < 5/6
Problem 7 :
Solution :
In the fractions 10/12 and 5/6, the denominators are different.
LCM of (12, 6) = 12
10/12 = (10 ∙ 1) / (12 ∙ 1) = 10/12
5/6 = (5 ∙ 2) / (6 ∙ 2) = 10/12
Compare the numerators of like fractions 10/12 and 10/12.
10/12 = 10/12
Substitute the corresponding original fractions.
10/12 = 5/6
Problem 8 :
Solution :
In the fractions 53/100 and 1/2, the denominators are different.
LCM of (100, 2) = 100
53/100 = (53 ∙ 1) / (100 ∙ 1) = 53/100
1/2 = (1 ∙ 50) / (2 ∙ 50) = 50/100
Compare the numerators of like fractions 53/100 and 50/100.
53/100 > 50/100
Substitute the corresponding original fractions.
53/100 > 1/2
Problem 9 :
Solution :
In the fractions 2/8 and 9/12, the denominators are different.
Make the denominators same using least common multiple.
LCM of (8, 12) = 24
2/8 = (2 ∙ 3) / (8 ∙ 3) = 6/24
9/12 = (9 ∙ 2) / (12 ∙ 2) = 18/24
Compare the numerators of like fractions 6/24 and 18/24.
6/24 < 18/24
Substitute the corresponding original fractions.
2/8 < 9/12
2/8 is less than 9/12
Problem 10 :
Solution:
In the fractions 1/6 and 3/12, the denominators are different.
LCM of (6, 12) = 12
1/6 = (1 ∙ 2) / (6 ∙ 2) = 2/12
3/12 = (3 ∙ 1) / (12 ∙ 1) = 3/12
Compare the numerators of like fractions 2/12 and 3/12.
2/12 < 3/12
Substitute the corresponding original fractions.
1/6 < 3/12
Problem 11 :
Solution :
In the fractions 4/5 and 77/100, the denominators are different.
LCM of (5, 100) = 100
4/5 = (4 ∙ 20) / (5 ∙ 20) = 80/100
77/100 = (77 ∙ 1) / (100 ∙ 1) = 77/100
Compare the numerators of like fractions 80/100 and 77/100.
80/100 > 77/100
Substitute the corresponding original fractions.
4/5 > 77/100
4/5 is greater than 77/100
Problem 12:
Solution :
In the fractions 1/3 and 5/12, the denominators are different.
LCM of (3, 12) = 12
1/3 = (1 ∙ 4) / (3 ∙ 4) = 4/12
5/12 = (5 ∙ 1) / (12 ∙ 1) = 5/12
Compare the numerators of like fractions 4/12 and 5/12.
4/12 < 5/12
Substitute the corresponding original fractions.
1/3 < 5/12
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