# Integer Representations

In this lesson, you will learn to describe conditions using opposites. Remember that two numbers are opposites if both are exactly the same distance from 0 on a number line. They are on opposite sides of the 0. We will be looking at the set of all whole numbers and their opposites. This group of numbers is known as integers.

Many situations in your life will be made up of both positive and negative numbers.

### Situation 1

One of the most common real life situations that involve negative and positive numbers will be money. You will deposit and withdraw money from your bank account. You will be paid money for work and you pay bills with that money. You may own stock and watch it go up one day and down the next.

Pat withdrew \$25 from her checking account and then deposited \$30. Is the overall change in the amount of money in her account positive, negative, or \$0? How do you know?

### Situation 2

Temperature may also be commonly represented by negative and positive numbers depending on the season and climate. The temperature on Monday was 5 . The temperature on Thursday was – 5. Was the overall change in the temperature positive, negative, or 0?

### Situation 3

Sea level is represented by 0 on a number line, and anything above sea level is assigned a positive number, while levels below that line are signified by negative numbers.

Larry dove to a depth of 10 feet below the surface of the water. He then swam 10 feet back up to the surface. Use integers to find the overall change in feet.

Comparing and ordering integers is simple when you use a number line. Remember that integers increase in value as you move to the right along a number line and decrease in value as you move in the left direction. When you are not looking for value, you can use measure distance on the number line. A number’s absolute value is its distance from 0 on a number line. Since distance can never be negative, absolute values are never negative. They are always positive or zero. The symbol for absolute value is | |.   |-5| is read as “the absolute value of negative 5.” For example 5 is the absolute value of 5. If more than one number is inside this symbol, treat it like a parenthesis. Evaluate the numbers inside the symbol, then express that value as a positive number. For example, |10 – 8|  simplifies to |2| which is 2.

## Integer Representations Practice

Find the overall change for each situation.

1. A football team loses 3 yards and then gains 3 yards.
2. Heather deposits \$25 in her account and then withdraws \$25 from her account.
3. A plane drops 300 feet in elevation and then rises 300 feet in elevation.

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