Objectives Add real numbers. Subtract real numbers.

The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|. 5 units 5 units - 6 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6 |–5| = 5 |5| = 5

Check It Out! Example 2a Add. –5 + (–7) –5 + (–7) = 5 + 7 When the signs are the same, find the sum of the absolute values. 5 + 7 = 12 Both numbers are negative, so the sum is negative. –12

Check It Out! Example 2b Add. –13.5 + (–22.3) When the signs are the same, find how many TOTAL NEG we have. –13.5 + (–22.3) –35.8 Both numbers are negative so, the sum is negative.

Check It Out! Example 2c Add. x + (–18) for x = -32 First substitute -32 for x. x + (–18) = -32 + (–18) –50 The sum is negative.

Check It Out! Example 2b Add. 11 + (–8) When the signs are the same, find how many TOTAL NEG we have. 11 + (–8) 3 Both numbers are negative so, the sum is negative.

Example 2B: Adding Real Numbers y + (-2) for y = -6 y + (2) = (-6) + (2) First substitute -6 for y. When the signs are the same, Find how many TOTAL NEG we have. (-6) + (2) -4 Both numbers are negative, so the sum is negative.

Check It Out! Example 2b Add. 8 + (–21) When the signs are the same, find how many TOTAL NEG we have. 8 + (–21) -29 Both numbers are negative so, the sum is negative.

Additive inverses 11 – 6 = 5 11 + (–6) = 5 A number and its opposite are additive inverses. To subtract signed numbers, you can use additive inverses. Subtracting 6 is the same as adding the inverse of 6. Additive inverses 11 – 6 = 5 11 + (–6) = 5 Subtracting a number is the same as adding the opposite of the number. (The both have a NEG sign right next to them)

Example 3A: Subtracting Real Numbers –6.7 – 4.1 –6.7 – 4.1 = –6.7 + (–4.1) Minus 4.1 is the same as -4.1 How many TOTAL NEG do you have? = –10.8 Both numbers are negative, so the sum is negative.

Check It Out! Example 3a Subtract. 13 – 21 Minus 21 is the same as -21 13 – 21 = 13 + (–21) When the signs of the numbers are different, see if you have more positives or more negatives. HOW MANY MORE ARE THERE? –8 The sum is negative.

Example 3B: Subtracting Real Numbers 5 – (–4) Two NEG signs are next to each Other so you can “blip blip” them to both be positive signs. 5 + (+4) = 5 + 4 9 Find the sum.

Example 3B: Subtracting Real Numbers 16 – (–10) Two NEG signs are next to each Other so you can “blip blip” them to both be positive signs. 16 + (+10) = 16 + 10 26 Find the sum.

Check It Out! Example 3c Subtract. x – (–12) for x = –14 x – (–12) = –14 – (–12) First substitute –14 for x. –14 + (+12) Two NEG signs are next to each Other so you can “blip blip” them to both be positive signs. –14 + 12 Are there more NEG or more POS? How many more? –2 The answer is negative.

Two numbers are opposites if their sum is 0 Two numbers are opposites if their sum is 0. A number and its opposite are on opposite sides of zero on a number line, but are the same distance from zero. They have the same absolute value.

Lesson Quiz Add or subtract using a number line. 2. –5 – (–3) –2 1. –2 + 9 7 Add or subtract. 3. –23 + 42 19 4. 4.5 – (–3.7) 8.2