COMPARING AND ORDERING FRACTIONS

Comparing Fractions

Whenever we compare two fractions, first we have to check the denominators.

Case 1 :

If the denominators are same, then we can decide that the fraction which is having the greater numerator is greater.

Case 2 :

If the denominators are different, then we have to make the denominators same and compare the fractions as said in case 1.

To make the denominator same, we have to apply the concept of least common multiple.

Ordering Fractions

To order fractions from least to greatest or greatest to least, first we have to check the denominators.

Case 1 :

If the denominators are same, then we can compare the values of the numerators and order the fractions.

Case 2 :

If the denominators are different, then we have to make the denominators same and order the fractions as said in case 1.

Find which fraction is greater :

Example 1 :

6/19 and 16/19

Solution :

In the fractions 6/19 and 16/19, the denominator is same. So, the fraction which has greater numerator will greater in value.

16/9 > 6/19

16/19 is greater than 6/19

Example 2 :

1/2 and 3/5

Solution :

In the fractions 1/2 and 3/5, the denominators are different.

Make the denominators same using least common multiple.

Least common multiple of (2, 5) = 10.

1/2 = (1 ⋅ 5)/(2 ⋅ 5) = 5/10

3/5 = (3 ⋅ 2)/(5 ⋅ 2) = 15/10

Compare the numerators of like fractions 5/10 and 15/10.

15/10 > 5/10

Substitute the corresponding original fractions.

3/5 > 1/2

3/5 is greater than 1/2

Example 3 :

7/12 and 11/18

Solution :

In the fractions 7/12 and 11/18, the denominators are different.

Make the denominators same using least common multiple.

Least common multiple of (12, 18) = 36.

7/12 = (7 ⋅ 3)/(12 ⋅ 3) = 21/36

11/18 = (11 ⋅ 2)/(18 ⋅ 2) = 22/36

Compare the numerators of like fractions 21/36 and 22/36.

22/36 > 21/36

Substitute the corresponding original fractions.

11/18 > 7/12

11/18 is greater than 7/12

Order the fractions from least to greatest :

Example 4 :

5/19, 7/19, 2/19, 3/19

Solution :

In all the given fractions, the denominator is same.

Compare the numerators and order them from least to greatest.

2/19, 3/19, 5/19, 7/19

Example 5 :

3/4, 2/5, 1/8

Solution :

In the given fractions, the denominators are different.

Make the denominator same using least common multiple and order them from least to greatest.

Least common multiple of (4, 5, 8) = 40.

3/4 = (3 ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

1/8 = (1 ⋅ 5)/(8 ⋅ 5) = 5/40

Compare the numerators of like fractions above and order them from least to greatest.

5/40, 16/40, 30/40

Substitute the corresponding original fractions.

1/8, 2/5, 3/4

Example 6 :

5/6, 1/4, 3/8, 7/12

Solution :

In the given fractions, the denominators are different. 

Make the denominator same using least common multiple and order them from least to greatest.

Least common multiple of (6, 4, 8, 12) = 24.

5/6 = (5 ⋅ 4)/(6 ⋅ 4) = 20/24

1/4 = (1 ⋅ 6)/(4 ⋅ 6) = 6/24

3/8 = (3 ⋅ 3)/(8 ⋅ 3) = 9/24

7/12 = (7 ⋅ 2)/(12 ⋅ 2) = 14/24

Compare the numerators of like fractions above and order them from least to greatest.

6/24, 9/24, 14/24, 20/24

Substitute the corresponding original fractions.

1/4, 3/8, 7/12, 5/6

Order the fractions from greatest to least :

Example 7 :

3/4, 2/5, 5/8, 1/2

Solution :

In the given fractions, the denominators are different.

Make the denominator same using least common multiple and order them from greatest to least.

Least common multiple of (4, 5, 8, 2) = 40.

3/4 = (3 ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

5/8 = (5 ⋅ 5)/(8 ⋅ 5) = 25/40

1/2 = (1 ⋅ 20)/(2 ⋅ 20) = 20/40

Compare the numerators of like fractions above and order them from greatest to least.

30/40, 25/40, 20/40, 16/40

Substitute the corresponding original fractions.

3/4, 5/8, 1/2, 2/5

Example 8 :

1/6, 1/3, 3/14, 2/7

Solution :

Make the denominator same using least common multiple and order them from greatest to least.

Least common multiple of (6, 3, 14, 7) = 42.

1/6 = (1 ⋅ 7)/(6 ⋅ 7) = 7/42

1/3 = (1 ⋅ 14)/(3 ⋅ 14) = 14/42

3/14 = (3 ⋅ 3)/(14 ⋅ 3) = 9/42

2/7 = (2 ⋅ 6)/(7 ⋅ 6) = 12/42

Compare the numerators of like fractions above and order them from greatest to least.

14/42, 12/42, 9/42, 7/42

Substitute the corresponding original fractions.

1/3, 2/7, 3/14, 1/6

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