Positive and Negative Numbers

Lesson 3.02

After completing this lesson, you will be able to say:

• I can use positive and negative numbers to represent quantities in the real world.

• I can recognize the meaning and direction of positive and negative numbers.

• I can explain the meaning of zero in real-world situations.

Key Words

Positive number:Any number that is greater than 0, such as 7, sometimes written with the + symbol, such as +7.

Negative number: Any number that is less than 0 and indicates an opposite value, written with the − symbol, such as −7.

Zero: A neutral number, which is neither negative nor positive, used to represent no value.

Positive and Negative Numbers

In a certain video game, players start with 0 points, and each time someone plays a new game, it resets to zero. After the first game, the player had a score of 35 points. After the second game, the player had a score of −10 points. Let's determine the meaning of zero points, positive points, and negative points in this game.

Zero means the player did not gain or lose any points overall. The player is back at the reset value.

Positive points means the player has an overall gain. So in the first game, the player had 35 points; this means that this player had a gain of 35 points from the reset score.

Negative points means the player had an overall loss. Because in the second game, the player had -10 points, this means the player had a loss of 10 points from the reset score.

Positive and Negative numbers – Try It!

When Sarah borrows $25 from her sister, her sister writes −$25 on a paper. Sarah paid her sister $15 one week; her sister wrote +$15 on the same paper.

What is the meaning of positive dollars, negative dollars, and 0 dollars?

Check your work

Positive+$15 means a gain of 15 dollars because it is a positive number.

Negative−$25 means a loss of 25 dollars because it is a negative number.

ZeroZero dollars would mean that Sarah does not owe her sister any money.

Temperature – Positive and Negative

Positive and negative numbers can work together to describe situations relating to temperature

In the summer, you may hear that it is 85°F outside. This means that it is 85 degrees above zero, since it is a positive number.

Remember, you do not always have to write the positive sign (+). A number with no sign is positive.

In this thermometer, you can see that the temperature is at negative 4°F (-4ºF) . So it is 4°F below zero.

Using positive and Negative numbers with Temperature

The lowest temperature of the day was 15°F below zero, and the highest temperature of the day was 3°F above zero. What is the low and high temperature?

Low: −15°F because you are told that it is below zero, it must be negative.

High: +3°F because you are told that it is above zero, it must be positive.

Try It

A weather woman recorded these temperatures in one day: Morning temperature: 0°FAfternoon temperature: +6.4°FNight temperature: −2.5°F

Which statements are true based on the recorded temperatures? • The afternoon temperature was 6.4 degrees above the

morning temperature. • The afternoon temperature was 6.4 degrees below the

morning temperature. • The night temperature was 2.5 degrees above the

morning temperature. • The night temperature was 2.5 degrees below the

morning temperature.

Check your work

Statements 1 and 4 are true. The morning temperature is zero. The afternoon temperature is 6.4°F above zero because it is positive, and the night temperature is 2.5°F below 0 because it is negative.

• The afternoon temperature was 6.4 degrees above the morning temperature.

• The night temperature was 2.5 degrees below the morning temperature.

Elevation – Positive and Negative Numbers

Elevation:

A measurement of the height of something above a certain zero level.

Elevation is used to measure the height of objects.

The elevation of something can also be measured above and below sea level. In this case, the surface of the sea is considered the zero value.

Examples of Elevation with Positive and Negative numbers

Mt. McKinley is the highest elevation and Death Valley is the lowest elevation in North America.

What is the meaning of zero, positive feet, and negative feet?

Location Elevation from Sea

Mt. McKinley +20,320 feet

Death Valley -282 feet

The zero would be the sea level, as that is where elevations were measured from.

The +20,320 feet means that it is 20,320 feet above sea level, as positive feet are measured above.

The −282 feet means that it is 282 feet below sea level, as negative feet are measured below.

Try it!

Place the scenarios in the correct box

The climber climbed 1500 feet up

The diver dove 15 feet

The swimmer is floating on the water

The elevator we up 13 floors

The temperature is -8 º F

Sally borrowed 10 dollars

Sally earned $10.00

Sally paid back the $10 she borrowed

Check your Work

Place the scenarios in the correct box

The climber climbed 1500 feet up

The diver dove 15 feet

The swimmer is floating on the water

The elevator we up 13 floors

The temperature is -8 º F

Sally borrowed 10 dollars

Sally earned $10.00

Sally paid back the $10 she borrowed

Above Zero

At Zero

Below Zero

Now that you completed this lesson, you should be able to say:

• I can use positive and negative numbers to represent quantities in the real world.

• I can recognize the meaning and direction of positive and negative numbers.

• I can explain the meaning of zero in real-world situations.