How do you subtract -14 - (-5) and how does that relate to distance?

In this lesson you will learn to subtract integers by using the

difference definition of subtraction on a number line.

Let’s ReviewLet’s Review

What’s an integer?Integers include positive and negative

whole numbers as well as 0. ...-3, -2, -1, 0, 1, 2, 3 ...

Non-Examples: -5.2 0.28 -9.9 4

Let’s ReviewLet’s Review

What’s subtraction?Subtraction is the opposite of addition.

15 - 3 = 12

minuend subtrahend difference

It can be seen as the process of taking away or finding the difference between two numbers.

Let’s ReviewLet’s Review

What’s distance?Distance is a measure of how far apart two things

are. Distance is always positive.

Let’s ReviewA Common Mistake

Thinking that difference is always positive.

3 - 8 = 5-3 - 8 = (-5)

Let’s ReviewCore Lesson710-3

3 106 - (-9)

9

-14 -5

-5 - (-14)

15

-9 6

Minuend - Subtrahend = Difference

Let’s ReviewCore Lesson73 - 10

3 10-9 - 6

9

-14 -5

-14 - (-5)

15

-9 6

-

-

-

Minuend - Subtrahend = Difference

Let’s ReviewCore Lesson710-3

3 106 - (-9)

9

-14 -5

-5 - (-14)

15

-9 6

Minuend - Subtrahend = Difference73 - 10

3 10-9 - 6

9

-14 -5

-14 - (-5)

15

-9 6

-

-

-

Minuend - Subtrahend = Difference

In this lesson you learned to subtract integers by using the

difference definition of subtraction on a number line.

Let’s ReviewGuided Practice

13 - (-5)Simplify 13 - (-5) and -5 - 13.

-5 - 13-5 13

-5 13

Let’s ReviewGuided Practice

4 - 10

Determine the difference: 4 - 10

Let’s ReviewExtension Activities

Think about the meaning of the words difference and distance in mathematics. Compare and contrast these words.

Difference Distance

Let’s ReviewExtension Activities

Fill out the following table. Then, describe how the A/B problem pairs relate in terms of difference and distance.

Problem A DifferenceDistance Between Integers

Ex: 5 - (-3) 8 8 13 - 8 -19 - (-4) -6 - 10

Problem B DifferenceDistance Between Integers

-3 - 5 -8 88 - 13

-4 - (-19)10 - (-6)

Let’s ReviewExtension Activities

In addition, the commutative property says that order doesn’t mater. Examine how order affects subtraction with these problems. What do you notice?

15 - 7 & 7 - 155 - (-14) & -14 - 5 .

-8 - 9 & 9 - (-8)-16 - (-6) & -6 - (-16)

22 - 22 & 22 - 22

Let’s ReviewQuick Quiz

Simplify 1 - (-8).

Determine the difference: 9 - 15.