Math Homework Help: Calculating Temperature

Help with Temperature

Temperature may be measured on the Celsius scale, which is commonly used in science. It's the standard temperature system used in many foreign countries as well. Temperatures can also be measured with the Fahrenheit system, which is typically used to report temperatures in the United States.

Temperature Ranges

Since temperatures fall very far below freezing in certain climates, both the Celsius and Fahrenheit scales include negative temperatures. For instance, your school might be closed if the temperature outside is -25 degrees Fahrenheit.

Word Problems with Temperature

Negative Integers

Since temperatures can be both negative and positive, you may be asked to solve word problems about calculating temperature differences between negative and positive integers. For example, imagine that you're given the following problem:

Today, the weather forecast reports that it's five degrees outside. The forecast says that the temperature will be seven degrees lower tomorrow. If the forecast is correct, what will the temperature be tomorrow?

To tackle this type of problem, you need to know how to add and subtract integers using a number line. This problem tells you that the starting point for the temperature is five degrees. Since tomorrow's temperature is expected to be seven degrees less, count seven degrees to the left from five on the number line. If you're working with a vertical number line, you'll count downward. You should arrive at negative two (5 - 7 = -2).

Absolute Value

You might also be asked to solve absolute value problems involving temperature. Absolute value is an integer's positive distance from zero. The absolute value of the number eight, for example, is eight, since that is its positive distance from zero. The absolute value of negative eight is also positive eight, since this is its positive distance from zero. Here's a sample temperature word problem that involves absolute value:

The average temperature in January was -12 degrees, while the average temperature in February was -15 degrees. What is the absolute value of the difference between the average temperatures in January and February?

One way to solve this problem is to use a number line or thermometer. This way, you can manually count and see that there is a difference of three degrees between the average temperatures for the two months. You can also solve the problem mathematically by calculating the difference in temperature and then finding the absolute value of this number. Here are the two methods:

One:

-15 - (-12) = -15 + 12 = -3

|-3| = 3 (The two vertical lines around the number is the symbol for absolute value.)

Two:

-12 - (-15) = -12 + 15 = 3

|3| = 3