Rounding fractions

Rounding fractions with and without a number line is the goal of this math lesson.

Example #1

The length of a desk is about 60 5/8 inches. What is the length of the desk to the nearest inch?

Solution

Look at the fraction part of 60 5/8 and decide if it is closer to 1 or closer to 0.

$Rounding fractions$

The fraction part of 60 5/8 is 5/8. Is 5/8 closer to 0 or 1? Looking at the number line above, we can see that 5/8 is closer to 1.

Therefore, to the nearest inch, the length of the desk is 61 inches.

Example #2

The depth of a three-seat sofa is about 32 1/8 inches. What is the depth of the three-seat sofa to the nearest 1/2 inch?

Solution

Look at the fraction part of 32 1/8 and decide if it is closer to 1/2 or closer to 0.

$Rounding fractions$

The fraction part of 32 1/8 is 1/8. Is 1/8 closer to 0 or 1/2? Looking at the number line above, we can see that 1/8 is closer to 0.

Therefore, to the nearest 1/2 inch, the depth of the three-seat sofa is 32 inches.

More examples showing how rounding fractions work

For the following examples, we will not use the number line. Just look at the fraction carefully before deciding which number it is closer to.

Example #3

The length of a math book is about 9 3/8 inches. What is the length of the math book to the nearest 1/2 inch?

Solution

3/8 is between 0 and 1/2. We need to determine if 3/8 is closer to 1/2 or closer to zero.

1/2 - 3/8 = 4/8 - 3/8 = 1/8

3/8 - 0 = 3/8

Since 1/8 is smaller than 3/8, 3/8 is closer to 1/2.

Since 3/8 is closer to 1/2, 3/8 rounded to the nearest 1/2 is 1/2. Therefore, 9 3/8 rounded to the nearest 1/2 is 9 1/2.

Example #4

The length of a car is about 14 7/9 feet. What is the length of the car to the nearest 1/2 foot?

Solution

7/9 is between 1/2 and 1. We need to determine if 7/9 is closer to 1/2 or closer to 1.

1 - 7/9 = 9/9 - 7/9 = 2/9 = 4/18

7/9 - 1/2 = 14/18 - 9/18 = 5/18

Since 4/18 is smaller than 5/18, 7/9 is closer to 1.

Since 7/9 is closer to 1, 7/9 rounded to the nearest 1/2 is 1. Therefore, 14 7/9 rounded to the nearest 1/2 is 15.