Cumulative Practice
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The absolute value of a number is its distance from 0 on the number line. Since distance is always greater than or equal to 0, the absolute value of any number is greater than or equal to 0.
D
We want to determine which list is ordered from least to greatest.
| List A | -| 3/4|, - 1/2, |3/8|, - 1/4, |- 7/8| |
|---|---|
| List B | - 1/2, - 1/4, |3/8|, -| 3/4|, |- 7/8| |
| List C | |- 7/8|, |3/8|, - 1/4, - 1/2, -| 3/4| |
| List D | -| 3/4|, - 1/2, - 1/4, |3/8|, |- 7/8| |
We can recall that the absolute value of a number is its distance from 0 on the number line. Since distance is always greater than or equal to 0, the absolute value of any number is greater than or equal to 0. The absolute value of a non-negative number is equal to the number, while the absolute value of a negative number is equal to its opposite.
First, we can simplify the numbers given in List A. -| 3/4|= - 3/4 - 1/2 |3/8|= 3/8 - 1/4 |- 7/8|= 7/8 We will plot the numbers on a number line to see the order from least to greatest.
The number that is the farthest to the left is - | 34|, so it is the least from the list. The farthest to the right is |- 78|, so it is the greatest. We can write the integers in order from least to greatest by moving from left to right on the number line. -| 3/4| , - 1/2 , - 1/4 , |3/8| , |- 7/8| This result corresponds to List D. This means that List D is ordered from least to greatest.