Absolute Values

Absolute Value

Module 1 Lesson 5

Standards for Mathematical Content

• A.SSE.2 - Use the structure of an expression to identify ways to rewrite it.

How can I meet this standard?

• I can evaluate expression that involve absolute value.

Poll

Will driving backwards change the milage?

• Yes

• No

Vocabulary

Absolute Value:

the distance a number is from zero on the number line.

Evaluating Expressions Involving Absolute Value

Go Over to Reveal Math

In Assignments do the "Learn • Evaluating Expressions Involving Absolute Value "

Write an Absolute Value Expression

Absolute value can represent the amount by which two quantities or measurements differ in size. If x and y represent two quantities or measurements, then |x - y | and |y - x | represent the distance between them, and thus represent the difference in size as a positive value.

Thermometers

The accuracy of a meat thermometer is the positive difference between the temperature reading on the thermometer t and the actual temperature of the meat m.

Let us see which expression are and are not equivalent to the accuracy of a meat thermometer.

• |m - t| : This expression is equivalent to the accuracy of a meat thermometer because it represents the difference between the measurements, and is always positive because it is the absolute value of the difference.

• |m| - |t| : This expression is not equivalent to the accuracy of a meat thermometer in all cases because if t > m then the value of this expression is negative

• |t - m| : This expression is equivalent to the accuracy of a meat thermometer because it represents the difference between the measurements, and is always nonnegative because it is the absolute value of the difference.

• |t| - |m| : This expression is not equivalent to the accuracy of a meat thermometer in all cases because if m > t then the value of this expression is negative

Adirondacks (left) Taconic (right)

Multiple Choice

A geologist wants to compare the heights above sea level of a mountaintop in the Adirondacks and one in the Taconic Mountains. If the height of the Adirondack peak a is greater than the height of the Taconic peak t, then which statement is not equivalent to the difference between the heights of the peaks?

• $\left|a-t\right|$

• $\left|t-a\right|$

• $\left|t\right|-\left|a\right|$

• $\left|a\right|-\left|t\right|$

| Absolute Value Symbols |

We treat absolute value symbols when evaluating expressions the same way we do with parentheses. We do all operations inside of the absolute value symbols first before we apply the absolute value symbol rule of making the value positive.

Open Ended

How would you evaluate

 $\left|-2\left(xy+5y\right)\right|$ 

Fill in the Blanks

Evaluate

 $\left|4y-3xy\right|\ if\ x=2\ and\ y=-2$  

Go Over to Reveal Math

In Assignment do the "Example 3 • Evaluate an Expression Involving Absolute Value "

Multiple Choice

Evaluate

 $2\left|6x-20\right|-4\ if\ x\ =\ 3$  

•  $-8$  

•  $-4$  

•  $0$  

•  $8$