Envision Math 2.0: Grade 6, Volume 1
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3. Absolute Values of Rational Numbers
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Exercise 44 Page 82

The amount owed is the absolute value of the negative account balance.

The Greater Number: Tom's
The Lesser Amount Owed: Tom's

Practice makes perfect

We are given Tom's and Marie's account balances.

Person Account Balance
Marie -$45.62
Tom -$42.55

We are asked to determine which balance represents the greater number and which balance represents the lesser amount owed. Let's first find the numbers that are represented by the balances.

Person Account Balance Number Represented by the Balance
Marie -$45.62 -45.62
Tom -$42.55 - 42.55

We can plot these numbers on a number line.

We can see that the number that represents the Tom's balance is to the right of Marie's. Therefore, Tom's balance represents the greater number. Greater number=-42.55 Now we will find the amounts owed by Tom and Marie. The amount owed is the absolute value of the negative account balance. Let's recall the definition of the absolute value.

Absolute Value of a Number

The distance between the number and 0 on a number line.

In other words, the absolute value of a number is the non-negative value of that number. The absolute value of a number a can be written as |a|. |a| = a and |- a| = a Let's find the absolute value of each account balance.

Person Account Balance Amount Owed
Marie -$45.62 |-$45.62|=$ 45.62
Tom's -$42.55 |-$42.55|=$ 42.55

We can see that Marie owes $45.62 and that Tom owes $42.55. This means that Tom's balance represents the lesser amount owed.