# 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
Credit: Edna Winti
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Aidin’s homework is to write about the world's highest geological feature. He discovered that Mount Everest reached 29,035 ft above sea level. Mauna Kea, only 13,796 ft above sea level. But since it started beneath the water, its total length from base to height was 33,476 ft. And the Mariana Trench is the deepest trench in the world at 36,070 ft! Which feature should Aidin write about?

In this concept, you will learn how to use integers to represent different situations in the real world.

### Integers to Represent Different Situations

There are many different kinds of numbers.

A whole number is any counting number. Numbers, like 1/2 or .75, that you use to describe a part of something are not whole numbers.

A positive number is a number greater than zero. It can be written with or without a + symbol in front of it. A gain in something is written with a positive number. Profit, increase, and income are all examples of words that mean positive.

A negative number is a number that is less than zero. It is always written with a - symbol in front of it. A loss is written with a negative number. Decrease, spend, and decline are examples of words that mean negative.

An integer is any positive whole number or its negative. Zero is also considered an integer.

Let's look at an example.

.

On this thermometer the temperature reads 100º. The temperature is above zero. That means that it is positive. Therefore, we can write it either as +100 or just as 100. A temperature that is below zero is negative. A temperature that is 5 degrees below zero, therefore, is written -5.

Here is another example.

Determine whether the integer given is positive or negative and write it out:

Sasha goes to the mall and spends 45.00 from her bank account at the clothing store. First, determine whether Sasha gains or loses money. Sasha "spends" this money, so she no longer has it. This makes it a loss. Then, write it as a negative integer. The answer is -45. ### Examples #### Example 1 Earlier, you were given a problem about Aidin and his science report. He has to choose between Mount Everest, at 29,035 ft above sea level, Mauna Kea which is 33,476 ft from its base to peak, but only 13,796 ft above sea level, and the Mariana Trench, which is actually the deepest point in the world, starting at 36,070 ft below sea level. His report is on the "highest" geological feature - which one does he write about? The "highest" geological feature is the one that stretches the farthest above sea level. In other words, the biggest integer. First, he writes them each as an integer. Mount Everest is 29,035 ft above sea level. "Above sea level" means it is positive. Then he writes it as a positive integer. Mount Everest is +29,035 Mauna Kea is trickier. It is 33,476 ft tall. But it is only 13,796 ft above sea level. That means it is 13,796ft positive. The rest of its length is beneath the water, below sea level, so it doesn't count. Then, he writes the part that is positive as a positive integer. Mauna Kea is +13,796 The Mariana Trench is 36,070 ft below sea level. "Below sea level" means that it is negative. Then, he writes it as a negative integer. The Mariana Trench is -36,070. Next, he writes them in a list to compare them. Mount Everest: +29,035 Mauna Kea: +13,796 The Mariana Trench: -36,070 Finally, he picks the one that is the biggest positive integer. That is Mount Everest. The answer is Mount Everest is the highest geological feature in the world. #### Example 2 People invest money in the stock market all the time. Sometimes the overall market increases and their money grows. Sometimes it decreases and they lose money. The amount of increase or decrease is characterized by positive or negative "points." Which of the following situations is expressed by a negative integer? 1. No gain or loss in the stock market There is no loss or gain. Therefore, the integer used to describe it is zero, which is neither negative nor is it positive. 1. The average plummeted 15 points The word "plummeted" indicates an extreme loss. Therefore, it would be written as -15. This is a negative integer, so it is the answer. 1. The overall rise was 30% The market is characterized as rising, which is positive. However, a percentage is not a whole number, so it is not an integer. Write out each of the following situations as an integer. #### Example 3 The head of the volcano is located 50 feet below sea level. First, determine whether the location is positive or negative. Sea level is zero in this example. That means that "below sea level" is negative. Then, write it as a negative integer. The answer is \begin{align*}-50\end{align*}. #### Example 4 Rahul spent100.00 on baseball cards.

First, determine whether Rahul gained or lost money.

He "spent" it. That means he no longer has it. So it is a loss.

Then, write it as a negative integer.

The answer is \begin{align*}-100\end{align*}.

#### Example 5

Alaska experienced a heat wave of \begin{align*}98^\circ\end{align*} on July 4th.

First, determine whether the temperature is above or below zero.

A "heat wave" means it's very hot. If it were below zero, it would be very cold. That means it is positive.

Then, write it as a positive integer.

The answer is \begin{align*}+98\end{align*}.

### Review

Write an integer to represent each situation.

1. A loss of 20 points
2. A gain of 14 points
3. A profit of $20.00 4. A loss of$18.00
5. An elevation of 500 ft.
6. 200 feet below sea level
7. 8 degrees below zero
8. 78 degrees
9. A decrease of $68.00 10. An increase of$55.00
11. The dow did not rise or fall today.
12. The plane descended at a rate of 15%.
13. The submarine surfaced.
14. The cost and the earnings evened out.
15. The stock market had an overall rate of 18% above.

To see the Review answers, open this PDF file and look for section 11.1.

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### Vocabulary Language: English

TermDefinition
Difference The result of a subtraction operation is called a difference.
Integer The integers consist of all natural numbers, their opposites, and zero. Integers are numbers in the list ..., -3, -2, -1, 0, 1, 2, 3...
Negative Numbers Negative numbers are numbers that are less than zero.
Positive Numbers Positive numbers are numbers that are greater than zero.