Absolute value comparisons

We have already learnt about the concept of absolute value, which tells us how far away a number is from zero.

Now we can use this knowledge to compare numbers. We can work out which values are larger/smaller, as well as which value is further away from zero. 

This is very useful because we can use it to compare positive and negative values in a meaningful way. For example, we can compare amounts of money (credit/debit), distances (particularly above and below sea level) and temperatures. 

Examples

Question 1

For each of the following select the largest value.

a. A) $\left|3\right|$|3|     B) $\left|-21\right|$|−21|     C) $-21$−21     D) $-7$−7

 

b. A) $\left|-18\right|$|−18|     B) $-17$−17     C) $24$24     D) $\left|-17\right|$|−17|

 

Question 2

Laura is in a hot air balloon $8.5$8.5m above sea level and Fred is exploring a cave $6.7$6.7m below sea level. Which of these statements are true?

A) Fred has greater elevation then Laura.

B) Fred is further from sea level than Laura.

C) Laura has greater elevation than Fred.

D) Laura is further from sea level than Fred.

 

Question 3

Ben has a bank account balance of -$\$29.50$$29.50. Brad has a bank account balance of $\$66.40$$66.40.

a. Who has the most money in their bank account?

b. Whose bank account is furthest from being at $\$0$$0?

c. If Brad gave all of the money in his bank account to Ben, would Ben be able to clear his debt?