**Ordering Fractions and Decimals Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on ordering fractions and decimals from least to greatest or from greatest to least.

Before look at the worksheet, if you would like to know, how to order fractions and decimals,

**Problem 1 : **

Order the following fractions from least to greatest :

17/24, 5/12, 9/16

**Problem 2 :**

Order the following values from greatest to least :

0.1, 7/10, 0.3

**Problem 3 :**

Order the following values from least to greatest :

3/4, 2/5, 0.125

**Problem 4 :**

Order the following values from least to greatest :

5/6, 0.375, 1/4

**Problem 5 : **

Order the following values from greatest to least :

1/20, 0.2, 0.074

**Problem 1 : **

Order the following fractions from least to greatest :

17/24, 5/12, 9/16

**Solution : **

**Step 1 :**

Convert all the fractions into like fractions.

We can use LCM method to make the denominators of the fractions same.

Here, the denominators are 24, 12 and 16.

LCM of (24, 12, 16) = 48

Now, make the denominators of all the fractions as 48 using multiplication.

17/24 = (17 ⋅ 2) / (24 ⋅ 2) = 28/48

5/12 = (5 ⋅ 4) / (12 ⋅ 4) = 20/48

9/16 = (9 ⋅ 3) / (16 ⋅ 3) = 27/48

**Step 2 :**

Now, compare the numerators of like fractions in step 1 and order them from least to greatest.

20/48, 27/48, 28/48

**Step 3 :**

Substitute the corresponding original fractions.

5/12, 9/16, 17/24

Therefore, the order of the given fractions from least to greatest is

5/12, 9/16, 17/24

**Problem 2 :**

Order the following values from greatest to least :

0.1, 7/10, 0.3

**Solution : **

**Step 1 :**

Convert the decimal numbers 0.1 and 0.3 into fractions.

0.1 = (0.1 ⋅ 10) / 10 = 1/10

0.3 = (0.3 ⋅ 10) / 10 = 3/10

**Step 2 :**

Substitute 1/10 for 0.1 and 3/10 for 0.3 in the given list of values.

Then, we have

1/10, 7/10, 3/10

**Step 3 :**

In the result of step 2, the fractions 1/10, 7/10 and 3/10 are all like fractions.

Because, all of them are having same denominator 10.

Now, compare the numerators of the fractions 1/10, 7/10 and 3/10 and order them from greatest to least.

7/10, 3/10, 1/10

**Step 5 :**

Substitute the corresponding original values.

7/10, 0.3, 0.1

Therefore, the order of the given values from greatest to greatest is

7/10, 0.3, 0.1

**Problem 3 :**

Order the following values from least to greatest :

3/4, 2/5, 0.125

**Solution : **

**Step 1 :**

Convert the decimal number 0.125 into a fraction.

0.125 = (0.125 ⋅ 1000) / 1000

0.125 = 125/1000

0.125 = 1/8

**Step 2 :**

Substitute 1/8 for 0.125 in the given list of values.

Then, we have

3/4, 2/5, 1/8

**Step 3 :**

Convert all the fractions in step 2 to like fractions.

We can use LCM method to make the denominators of the fractions same.

Here, the denominators are 4, 5 and 8.

LCM of (4, 5, 8) = 40

Now, make the denominators of all the fractions as 40 using multiplication.

3/4 = (3 ⋅ 10) / (4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8) / (5 ⋅ 8) = 16/40

0.125 = 1/8 = (1 ⋅ 5) / (8 ⋅ 5) = 5/40

**Step 4 :**

Now, compare the numerators of like fractions in step 3 and order them from least to greatest.

5/40, 16/40, 30/40

**Step 5 :**

Substitute the corresponding original values.

0.125, 2/5, 3/4

Therefore, the order of the given values from least to greatest is

0.125, 2/5, 3/4

**Problem 4 :**

Order the following values from least to greatest :

5/6, 0.375, 1/4

**Solution : **

**Step 1 :**

Convert the decimal number 0.375 into a fraction.

0.375 = (0.375 ⋅ 1000) / 1000

0.375 = 375/1000

0.375 = 3/8

**Step 2 :**

Substitute 3/8 for 0.375 in the given list of values.

Then, we have

5/6, 3/8, 1/4

**Step 3 :**

Convert all the fractions in step 2 to like fractions.

We can use LCM method to make the denominators of the fractions same.

Here, the denominators are 6, 8 and 4.

LCM of (6, 8, 4) = 24

Now, make the denominators of all the fractions as 24 using multiplication.

5/6 = (5 ⋅ 4) / (6 ⋅ 4) = 20/24

0.375 = 3/8 = (3 ⋅ 3) / (8 ⋅ 3) = 9/24

1/4 = (1 ⋅ 6) / (4 ⋅ 6) = 6/24

**Step 4 :**

Now, compare the numerators of like fractions in step 3 and order them from least to greatest.

6/24, 9/24, 20/24

**Step 5 :**

Substitute the corresponding original values.

1/4, 0.375, 5/6

Therefore, the order of the given values from least to greatest is

1/4, 0.375, 5/6

**Problem 5 : **

Order the following values from greatest to least :

1/20, 0.2, 0.074

**Solution : **

**Step 1 :**

Convert all the decimal numbers 0.2 and 0.074 into fractions.

0.2 = (0.2 ⋅ 10) / 10 = 2/10 = 1/5

0.074 = (0.074 ⋅ 1000) / 1000 = 74/1000 = 37/500

**Step 2 :**

Substitute 1/5 for 0.2 and 37/500 for 0.74 in the given list of values.

Then, we have

1/20, 1/5, 37/500

**Step 3 :**

Convert all the fractions in step 2 into like fractions.

We can use LCM method to make the denominators of the fractions same.

Here, the denominators are 20, 5 and 500.

LCM of (20, 5, 500) = 500

Now, make the denominators of all the fractions as 500 using multiplication.

1/20 = (1 ⋅ 25) / (20 ⋅ 25) = 25/500

0.2 = 1/5 = (1 ⋅ 100) / (5 ⋅ 100) = 100/500

0.074 = 37/500 = (37 ⋅ 1) / (500 ⋅ 1) = 37/500

**Step 3 :**

Now, compare the numerators of like fractions in step 2 and order them from greatest to least.

100/500, 37/500, 25/500

**Step 4 :**

Substitute the corresponding decimals.

0.2, 0.074, 1/20

Therefore, the order of the given decimal numbers from least to greatest is

0.2, 0.074, 1/20

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

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