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# Integers that Represent Different Situations

## Write variable expressions to represent word problems including positives and negatives

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Integers that Represent Different Situations
License: CC BY-NC 3.0

Michele lives in Salt Lake City, Utah. In school she learned that Salt Lake City is 4,300 feet above sea level. Michele is going on vacation with her family to Death Valley in California. Her mom told her that Death Valley has the lowest land in North America and a portion of it lies 282 feet below sea level. How could Michele represent the locations of Salt Lake City and Death Valley with respect to sea level using integers?

In this concept, you will learn how to write integers to represent real world situations.

### Writing Integers to Represent Real World Situations

Integers are a set of numbers that include the positive whole numbers (1, 2, 3, 4, 5, ...), their opposites (-1, -2, -3, -4, -5, ...) and zero. This number line shows the integers from -5 to 5.

License: CC BY-NC 3.0

You can use integers to help represent many real world situations, such as:

• Increases and decreases in temperature.
• Profits and losses of money
• Locations above and below sea level.

Let's look at an example.

Suppose the temperature outside a ski lodge was 3F\begin{align*}3^\circ F\end{align*} below 0F\begin{align*}0^\circ F\end{align*}. You want to express that temperature with an integer.

To write this as an integer, first you should look for key words. The word “below” means the integer will be negative. Therefore, the temperature is 3F\begin{align*}-3^\circ F\end{align*} .

Let's look at another example.

A fisherman is sitting 2 feet above the surface of a lake on a boat. The hook on his fishing pole is floating 6 feet below the lake’s surface. Use integers to represent the position of the fisherman and his hook.

The surface of the lake can be represented by the integer 0.

The fisherman is sitting above the surface. The word “above” means the integer will be positive. The position of the fisherman is +2 or 2.

The hook is floating below the surface. The word “below” means the integer will be negative. You can represent the position of the hook as -6.

### Examples

#### Example 1

Earlier, you were given a problem about Michele, who was traveling to Death Valley.

Michele knows that Salt Lake City is 4,300 feet above sea level, while parts of Death Valley are 282 feet below sea level. Michele wanted to figure out how to represent these locations with respect to sea level using integers.

First, consider Salt Lake City. It is above sea level so you will use a positive integer. With respect to sea level, Salt Lake City is +4,300 or 4,300.

Next, consider Death Valley. It is below sea level so you will use a negative integer. With respect to sea level, Death Valley is -282.

The answer is 4,300 for Salt Lake City and -282 for Death Valley.

#### Example 2

Express the following situation using integers.

John gained 15 dollars, but then he lost 20 dollars.

First, look for key words in order to determine if your integers will be positive or negative. To “gain” means to get more, so that will be a positive integer. “Lost” means to have less, so that will be a negative integer.

Now, you can write your answer:

+15 represents the gain.

-20 represents the loss.

The answer is +15 gain and -20 loss.

#### Example 3

Express the following using an integer.

An increase of 200.00. First, look for key words. The word “increase” means to go up, so you will use a positive integer. The answer is +200 or 200. #### Example 4 Express the following using an integer. Down 10%. First, look for key words. The word “down” means you will need to use a negative integer. The answer is -10%. #### Example 5 Express the following using an integer. 50 feet below sea level. First, look for key words. The word “below” means you will need to use a negative integer. The answer is -50. ### Review Write each as an integer. 1. 10 degrees below zero 2. 50F\begin{align*}50^\circ F\end{align*} 3. A loss of20.00
4. 35 feet below the surface
5. 120 feet below sea level
6. An altitude of 15,000 feet

Use two integers and an operation to represent each situation.

1. A loss of 20 and a gain of 15.
2. A gain of 15, then a loss of twenty.
3. A gain of 20 and a gain of 35.
4. A loss of 19 and another loss of 30.
5. An altitude of 30,000 feet and another height of 15,000 feet
6. A loss of 15,000 feet and another loss of 12,000 feet.
7. A depth of 60 feet and a resting stop at 15 feet below the surface of the water.
8. A depth of 15 feet and then another descent of 20 feet below the surface of the water.
9. The hikers climbed to 1500 feet and then hiked another 1000 feet.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.1.

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### Vocabulary Language: English

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).

Difference

The result of a subtraction operation is called a difference.

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.

Whole Numbers

The whole numbers are all positive counting numbers and zero. The whole numbers are 0, 1, 2, 3, ...

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1. [1]^ License: CC BY-NC 3.0
2. [2]^ License: CC BY-NC 3.0

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