COMPARING AND ORDERING RATIONAL NUMBERS WORKSHEET

Problem 1 :

Find which of the given two fractions is greater :

6/19 and 16/19

Solution :

6/19 and 16/19

Since the denominators of those fractions are same, compare the numerators.

6 < 16

So, 16/19 is greater than 6/19.

Problem 2 :

Find which fraction is greater :

1/2 and 3/5

Solution :

1/2 and 3/5

For the given two fractions, the denominators are different. Make the denominator of each fraction same using least common multiplication of the denominators.

Lest common multiple of (2, 5) is 10.

1/2 = (1 x 5)/(2 x 5) = 5/10

3/5 = (3 x 2)/(5 x 2) = 6/10

Since the denominators of the two fractions 5/10 and 6/10 are same, compare the numerators.

5 < 10

5/10 < 6/10

Substitute the corresponding original fractions.

1/2 < 3/5

So, 3/5 is greater than 1/2.

Problem 3 :

Compare 1.031 and 0.256.

Solution :

1.031 and 0.256

To compare the given decimal numbers, we have to write them in a table as given below.

In the above table, compare the numbers in the first column (units).

We have 1 in 1.0231 and 0 in 0.256.

Because 1 is greater than 0, we have

1.031 is greater than 0.256

Problem 4 :

Compare 0.231 and 0.228.

Solution :

0.231 and 0.228

To compare the given decimal numbers, we have to write them in a table as given below.

In the above table, compare the numbers in the first column (units).

In the first column, we have have 0 in both the decimal numbers 0.231 and 0.228.

So, we have to compare the numbers in the third column (Tenths).

In the third column (Tenths), we have the same number 2 in both the decimal numbers.

So, we have to compare the numbers in fourth column (Hundredths).

In the fourth column (Hundredths), we have 3 in 0.231 and 2 in 0.228.

Since 3 is greater than 2, we have

0.231 is greater than 0.228

Problem 5 :

 Order the fractions from least to greatest : 

3/4, 2/5, 1/8

Solution :

3/4 , 2/5, 1/8

For the given fractions, the denominators are different. Make the denominator of each fraction same using least common multiplication of the denominators.

Lest common multiple of (2, 5, 8) is 40.

3/4 = (3 x 10)/(4 x 10) = 30/40

2/5 = (2 x 8)/(5 x 8) = 16/40

1/8 = (1 x 5)/(8 x 5) = 5/40

Since the denominators of the fractions 3/40, 16/40 and 5/40 are same, compare and order the numerators from least to greatest.

5/40 < 16/40 < 30/40

Substitute the corresponding original fractions.

1/8 < 2/5 < 3/4

Problem 6 :

Order the decimal numbers 1.023, 1.101 and 0.985 from least to greatest.

Solution :

1.023, 1.101, 0.985

To order the given decimal numbers, first we have to write them in a table as given below.

To get the least one, compare the numbers in the first column (units).

We get 0 in 0.985. This is the least among the given three decimal numbers.

To get the next least number, let us compare 1.023 and 1.101.

In both the decimals, we find 1 in the first column (units).

Now, we have to compare the third column (Tenths). There we get 0 in 1.023 and 1 in 1.101.

Since 0 is less than 1, the next least decimal is 1.023.

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

0.985, 1.023, 1.101

Problem 7 :

Five friends completed a triathlon that included a 3-mile run, a 12-mile bike ride, and a 1/2 -mile swim. To compare their running times they created a table that shows the difference between each person’s time and the average time, with negative numbers representing times less than the average.

Use a number line to order the numbers from greatest to least.

Solution :

Step 1 :

Write the fractions as equivalent decimals.

1/2 = 0.5 and -1 1/4 = -1.25

Step 2 :

Use the number line to write the decimals in order.

From the above number line, we have the numbers in order from greatest to least are

1.95, 1.4, 1/2, -1 1/4, -2.0

Problem 8 :

You, your sister, and a friend each take the same number of shots at a soccer goal. You make 72% of your shots, your sister makes 19/25 of her shots, and your friend makes 0.67 of his shots. Who made the fewest shots?

Solution :

Number of shots you make = 72%

= 72/100

= 0.72

Number of shots your sister make = 19/25

Converting the denominator by 100.

= (19/25) x (4/4)

= 76/100

= 0.76

Numbe of shots your friend make = 0.67

Comparing 0.67, 0.72 and 0.76, 0.67 is smallest. Then your friend made lesser shots.

Problem 9 :

You make 75% of your shots, your sister makes 13/20 of her shots, and your friend makes 0.7 of his shots. Who made the most shots?

Solution :

Number of shots you make = 75%

= 75/100

= 0.75

Number of shots your sister make = 13/20

Converting the denominator by 100.

= (13/20) x (5/5)

= 65/100

= 0.65

Numbe of shots your friend make = 0.7

Comparing 0.65, 0.7 and 0.75, 0.65 is smallest. Then your sister made lesser shots.

Problem 10 :

The map shows the portions of the population of Florida that live in five counties. List the five counties in order by population from least to greatest.

Solution :

Population in

Esxambia = 1/50

= (1/50) x (2/2)

= 2/100

= 0.02

Pinellas = 1/20

= (1/20) x (5/5)

= 5/100

= 0.05

Orange = 0.06

Palm beach = 7%

= 7/100

= 0.07

Miami dade = 0.13

Arranging the numbers from least to greatest,

0.02, 0.05, 0.06, 0.07, 0.13

Esxambia, Pinellas, Orange, Palm beach, Miami dade

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