**Ordering Fractions with Different Denominators :**

In this section, you will learn, how to order fractions with different denominators.

To order fractions in the order from least to greatest or greatest to least, the denominators must be same.

To order fractions with different denominators, we have to follow the steps given below.

**Step 1 :**

Find the least common multiple (LCM) of all the denominators.

**Step 2 :**

**Mae the result of step 1 (LCM) as denominator for each fraction using multiplication.**

**Step 3 :**

**In step 2, all the fractions will be like fractions (Having same denominator). **

**Now, you can compare the values of numerators and order the fractions from least to greatest or greatest to least. **

**Step 4 : **

Substitute the corresponding original fractions in the order.

**Question 1 :**

Order the following fractions in the order from least to greatest :

3/4, 5/8, 11/12

**Solution :**

**Step 1 : **

Find least common multiple of the denominators.

LCM of (4, 8, 12) = 24

**Step 2 : **

Make each denominator as 24 using multiplication.

3/4 = (3 ⋅ 6) / (4 ⋅ 6) = 18/24

5/8 = (5 ⋅ 3) / (8 ⋅ 3) = 15/24

11/12 = (11 ⋅ 2) / (12 ⋅ 2) = 22/24

**Step 2 : **

Compare the numerators in the like fractions in step 2 and order them from least to greatest.

15/24, 18/24, 22/24

**Step 3 : **

Substitute the corresponding original fractions.

5/8, 3/4, 11/12

**Question 2 :**

Order the following fractions in the order from least to greatest :

3/4 , 2/5, 1/8

**Solution :**

**Step 1 : **

Find least common multiple of the denominators.

LCM of (4, 5, 8) = 40

**Step 2 : **

Make each denominator as 24 using multiplication.

3/4 = (3 ⋅ 10) / (4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8) / (5 ⋅ 8) = 16/40

1/8 = (1 ⋅ 5) / (8 ⋅ 5) = 5/40

**Step 2 : **

Compare the numerators in the like fractions in step 2 and order them from least to greatest.

5/40, 16/40, 30/40

**Step 3 : **

Substitute the corresponding original fractions.

1/8, 2/5, 3/4

**Question 3 :**

Order the following fractions in the order from least to greatest :

11/15 , 7/12, 17/20

**Solution :**

**Step 1 : **

Find least common multiple of the denominators.

LCM of (15, 12, 20) = 60

**Step 2 : **

Make each denominator as 24 using multiplication.

11/15 = (11 ⋅ 4) / (15 ⋅ 4) = 44/60

7/12 = (7 ⋅ 5) / (12 ⋅ 5) = 35/60

17/20 = (17 ⋅ 3) / (20 ⋅ 3) = 51/60

**Step 2 : **

Compare the numerators in the like fractions in step 2 and order them from least to greatest.

35/60, 44/60, 51/60

**Step 3 : **

Substitute the corresponding original fractions.

7/12, 11/15, 51/60

After having gone through the stuff given above, we hope that the students would have understood, how to order fractions with different denominators.

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