1. Section 1-5 Subtracting Real Numbers SPI 12C: Add and subtract algebraic expressions. Objectives: Subtract real numbers using models and rules A runner starts out running at a distance of 20 miles from her house. She runs in the direction of her house for 30 miles. How many miles did she run past her house? -20 -10 0 10 20

2. Modeling Subtraction of Real Numbers 1. Model using number lines 2. Model using Algebra Tiles 3. Model using Matrices Subtract –3 – 2 using a number line. Start at –3. Move left 2 units Subtract Integers using a Number Line 4. Model using numbers and operation symbols

3. Subtract 4 – (–2) using tiles. There are 6 positive tiles left. Start with 4 positive tiles.Add zero pairs until there are 2 negative tiles. Remove 2 negative tiles. Subtract Integers using Algebra Tiles

4. -3 - 57 - 10 Subtract Integers using Matrices 5 12 –3 7 4 6 5 10 – 1 6 –8 –3 = Subtract the two matrices. Remember to subtract the numbers in corresponding positions and place answers in a new matrix in corresponding positions. 5 – 4 12 - 6 =

5. Simplify –11.6 – (–14). –11.6 – (–14) = –11.6 + 14The opposite of –14 is 14. = 2.4Add. Subtract Integers using Numbers and Operations Symbols Simplify |–13 – (–21)|. |–13 – (–21)| = | –13 + 21| The opposite of –21 is 21. = | 8 |Add within absolute value symbols. = 8Find the absolute value. Rule for Subtracting Numbers To subtract a number, add its opposite. Examples: 3 – 5 = 3 + (-5) = -2 3 – (- 5) = 3 + 5 = 8

6. The temperature in Montreal, Canada, at 6:00 P.M. was –8°C. Find the temperature at 10:00 P.M. if it fell 7°C. Find the temperature at 10:00 P.M. by subtracting 7°C from the temperature at 6:00 P.M. –8 – 7 = –8 + (–7)Add the opposite. = –15Simplify. The temperature at 10:00 P.M. was –15°C. Real-world example Evaluate x – (–y) for x = –3 and y = –6. x – (–y) = –3 – [–(–6)]Substitute –3 for x and –6 for y. = –3 – 6The opposite of –6 is 6. = –9Subtract.