Step Up to High School Math
Lesson 3
Subtracting Real Numbers
Lesson Objectives
  I can add and subtract real numbers using a number line,
Rules of Addition and Subtraction and the Additive Inverse.
  Student actions
  Students will use a number line to subtract real numbers
  Student will apply the subtraction rule to evaluate variable
expressions
  Students will apply the subtraction rule to evaluate change in
values using real life situations
  Students will apply the Additive Inverse and the Rules of
Addition to to justify the reasonableness of their differences
when subtracting Real Numbers
Think about this!
  Your parents buy you a laptop for $1340.You agree to pay
them back by working around the house.
  Each week you earn $40 for working outside the house and
$25 for working inside the house.
  Questions (Write in complete sentences.)
  How can you determine if the amount you owe your parents is
positive or negative?
Review Vocabulary
  Additive Identity
  The number 0 is the additive identity in an addition problem

3+0=3
  Additive Inverse
  The opposite of a number a is the additive inverse.
Using a Number Line
  When using a number line, it is important to understand that
the positive and negative sign tells you the direction to move.
  Subtraction is the opposite of addition, so:
  If you are subtracting a positive number, you will move to the
left.
  If you are subtracting a negative number, you will move to the
right
  The first number is your starting point. The second number
is how many spaces you will move. The answer is your ending
point.
Using a Number line
  Use a number line to find the sum of the following:

(+5) - (+10) =
Start at 5, since 10 is positive move 10 spaces to the left.
  (-5) - (-10) =
  Start at -5, since 10 is negative, move to spaces to the right.
Rules for Subtracting Real Numbers
  To subtract a from b, add the opposite (the additive inverse)
of b to a, then follow the Rules of Addition for Real
Numbers.
  Example:
  a – b = a + (-b) {The opposite of b is (-b)}
  3 – 5 = 3 + (-5) =
  a – (- b ) = a + b {The opposite of (-b) is b}
  3 – (-5) = 3 + 5 =
  -a – b = -a + (-b) {notice the first number does not change}
  -3 – 5 = -3 + (-5) =
  -a – (-b) = -a + b {notice the first number does not change}
  -3 – (-5) = -3 + 5 =
Rules of Addition
  Same Signs
  To add two numbers with the same signs, add their absolute
values and keep the sign.
  Different Signs
  To add two numbers of different signs, subtract the absolute
value of the smaller number from the absolute value of the
larger number.
  The sum has the same sign as the the number with the larger
absolute value
Properties of Addition
  Identity Property
  The sum of any number and 0 is the number

125 + 0 = 125
X+0=X
  Inverse Property
  The sum of any number and its opposite is 0.


125 + (- 125) = 0
3 + (-3) = 0
Example 1: Add Real Numbers
  Use a number line to find the sum of the following:
  1. 7 - (-2)
2. 2 - 7
Subtracting Real Numbers
  Use the Subtraction Rule to find the difference of the
following:

12 – (-8) =

- 15 – 11 =
Evaluate a variable expression
  Use the subtraction to evaluate the expression below
  x – 5.1 – y
  Let x = 3.7 and y = −2.3
Evaluate Change
  A Share of a stock on the New York Stock Exchange was
valued at $31.26at the opening of trading. The value of the
stock at closing was $27.97
  Step 1
  Write a verbal model for the situation
Solve a Multi-Step Problem
  Step 2
  Find the Change in Value
  Change in value =
Guided Practice
  Work with your partner to complete these guided practice
problems.
1)  −9 − (−3)
2)  17 − 21
3)  23 − (−7)
4)  −7 − 6 − (−9)
5)  x + y − 7 {Let x = −5 and y = 3}
6)  Find the change from 12°F to −2°F
7)  Find the change from −8°F to 21°F
Summary
  Your parents buy you a laptop for $1340.You agree to pay
them back by working around the house.
  Each week you earn $40 for working outside the house and
$25 for working inside the house.
  Questions (Write in complete sentences.)
  How can you find your balance at the end of Week 1 if you only
work outside?
  How can you find your balance at the end of Week 2 if you work
both inside and outside?
Summary
  Jayden says that −11 −4 = −15. His sister Jaylen argues that
the answer is −7. Who is correct? Justify your answer by
using the number line, the additive inverse or the subtraction
rule.
Exit Pass
  Complete your exit pass and hand it to me before leaving. If
you complete your exit pass before the class ends, you may
begin your homework.