ALGEBRA 1

Lesson 1-4 Warm-Up

ALGEBRA 1

Lesson 1-4 Warm-Up

ALGEBRA 1

“Adding Real Numbers” (1-4) What is the “Identity Property of Addition”?

What is the “Inverse Property of Addition”?

How can you use a number line to add integers?

identity Property of Addition: A number plus 0 is equal to the original number [In other words, the number keeps its identity (doesn’t change) when 0 is added to it.]Examples: 5 + 0 = 5 n + 0 = n

Inverse Property of Addition: A number plus its additive inverse (its opposite = same number with the opposite sign) is equal to zero.Examples: 17 + (-17) = 0 n + (-n) = 0

To add integers using a number line, start at the first number and move / jump the number of units right (+) or left (-) the second number tells you to.Examples: (see next slide)

ALGEBRA 1

Use a number line to simplify each expression.

a. 3 + (–5)

3 + (–5) = –2

b. –3 + 5

–3 + 5 = 2

Start at 3.Move left 5 units.

Start at –3.Move right 5 units.

c. –3 + (–5)–3 + (–5) = –8

Start at –3.Move left 5 units.

Adding Real NumbersLESSON 1-4

Additional Examples

ALGEBRA 1

“Adding Real Numbers” (1-4) What are the rules for adding integers with the same and different signs?

Rule: Adding Numbers With the Same Signs – To add two numbers with the same signs, add their absolute values (add them) and use the same sign as both the addends (the numbers you’re adding)Examples: 2 + 6 = 8 -2 + (-6) = -8

Rule: Adding Numbers With Different Signs – To add two numbers with different signs, find the difference of their absolute values (subtract them) and use the same sign as the addend with the greatest absolute value (take the sign from the bigger number).Examples: -2 + 6 = 4 2 + (-6) = -4

ALGEBRA 1

Simplify each expression.

a. 12 + (–23) = –11

b. –6.4 + (–8.6) = –15.0

The difference of the absolute values is 11. The negative addend has the greater absolute value (|-23| is bigger than |12|), so the sum is negative.

Since both addends are negative, add their absolute values (6.4 and 8.6). The sum is also negative.

Adding Real NumbersLESSON 1-4

Additional Examples

ALGEBRA 1

The water level in a lake rose 6 inches and then fell 11 inches. Write an addition statement to find the total change in water level.

6 + (–11) = –5   The water level fell 5 inches.

Adding Real NumbersLESSON 1-4

Additional Examples

ALGEBRA 1

Evaluate 3.6 + (–t) for t = –1.7.

= 3.6 + [–(–1.7)] Substitute –1.7 for t.

= 3.6 + [1.7] –(–1.7) means the opposite of –1.7, which is 1.7.

= 5.3 Simplify.

Adding Real NumbersLESSON 1-4

Additional Examples

ALGEBRA 1

A scuba diver who is 88 ft below sea level begins to ascend to the surface.

Define: Let r = the number of feet the diver rises.

a.  Write an expression to represent the diver’s depth below sea level after rising any number of feet.

Equation: –88 + r–88 + r

b.  Find the new depth of the scuba diver after rising 37 ft.–88 + r = –88 + 37 Substitute 37 for r.

= – 51 Simplify.The scuba diver is 51 ft below sea level.

Words: 88 ft below sea level  plus  feet diver rises  

Adding Real NumbersLESSON 1-4

Additional Examples

ALGEBRA 1

Simplify.

1. 15 + (– 10) 2. – 57 + (– 11) 3. – 42 + 19

4. – 1 + (– 3 )

Evaluate each expression for x = –5.

5. – 11 + (– x)

6. 25 + 4x

5 –68 –23

–4 715

15

4 15

5

– 6

Adding Real NumbersLESSON 1-4

Lesson Quiz