Section 1-5 Subtracting Real NumbersSPI 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

Modeling Subtraction of Real Numbers

1. Model using number lines2. Model using Algebra Tiles3. 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

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

-3 - 5 7 - 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

=

Simplify –11.6 – (–14).

–11.6 – (–14) = –11.6 + 14 The opposite of –14 is 14.

= 2.4 Add.

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.

= 8 Find the absolute value.

Rule for Subtracting NumbersTo subtract a number, add its opposite.

Examples: 3 – 5 = 3 + (-5) = -2 3 – (- 5) = 3 + 5 = 8

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.

= –15 Simplify.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 – 6 The opposite of –6 is 6.

= –9 Subtract.