Geometry Essentials - Integers and Absolute Value

Flashcards covering definitions and operations for integers, opposites, and absolute values based on the Geometry Essentials Week 3 Day 1 lecture.

What is the definition of an integer?

The set of whole numbers and their opposites, such as $-3, -2, -1, 0, 1, 2, 3$.

How are opposites defined in relation to a number line?

Two numbers that are the same distance from $0$ on a number line, but on opposite sides of $0$.

What is the "net worth" of opposite integers?

The "net worth" of opposite integers is zero.

How is absolute value defined?

The distance between a number and $0$ on a number line.

What is the notation used to write the absolute value of a number $a$?

$$|a|$$

Evaluate the absolute value of $-5$.

$$|-5| = 5$$

Evaluate the absolute value of $-297$.

$$297$$

What is the rule for adding integers with the same sign?

Add the absolute values of the integers and then use the common sign.

What is the rule for adding integers with different signs?

Subtract the lesser absolute value from the greater absolute value, then use the sign of the integer with the greater absolute value.

According to the rules for subtracting integers, how do you subtract an integer?

To subtract an integer, add its opposite.

In which direction do you move on a number line to add and to subtract?

To add, move right; to subtract, move left.

What is Rule 1 for adding and subtracting integers?

Adding a negative is the same as subtracting a positive.

What is Rule 2 for adding and subtracting integers?

Subtracting a negative is the same as adding a positive.

Evaluate the expression $5 + (-11)$.

$$-6$$

What is the result of $15 - (-10)$?

$$25$$

Evaluate the expression $-11 - 11$.

$$-22$$

Simplify the expression $| -15 - 9 |$.

$$24$$

Simplify the expression $| -24 - (-19) |$.

$$5$$

According to the lecture strategy, what three questions should you ask when adding or subtracting integers?

1. Am I starting with a positive or a negative? 2. Am I making it bigger or smaller? 3. Will my answer be positive, negative, or zero?