Lesson
7 Subtracting Positive Integers
Subtracting Positive Integers
How is adding the opposite connected to
subtraction?
We learned how to write addition and subtraction fact families.
We know that there is a unique relationship between addition and
subtraction.
Here is the fact family for the numbers 7, 8, and 15.
Fact Family for 7, 8, and 15
7 + 8 = 15
8 + 7 = 15
15 − 8 = 7
15 − 7 = 8
Now that we learned about positive and negative integers, we can
extend our thinking about subtraction. Subtraction is the same
as “adding the opposite.”
Subtracting With Positive Integers
When we first learned about subtraction, we put a group of objects
together, then we removed the ones we were subtracting.
The equation 5 − 2 = 3 looks like this:
Let’s see how 5 − 2 = 3 is the same as 5 + −2 = 3.
Unit 8 • Lesson 7 571
Lesson 7
Example 1
Show that 5 − 2 = 3 is the same as 5 + −2 = 3.
Using the black and red cards helps us see how addition with a negative
is the same as subtracting two positive integers.
Let’s look at 5 + −2.
d ​5 (positive) = 5 black cards
d ​−2 (negative) = 2 red cards
We cancel out 2 black cards (positive) with 2 red cards (negative).
The equation 5 − 2 = 3 is the same as 5 + −2 = 3.
The process is a little different, but the results are the same. In both
cases, we end up “taking away 2” and we are left with 3. Let’s look at
another example.
Example 2
Show that 4 − 3 = 1 is the same as 4 + −3 = 1.
d ​4 (positive) = 4 black cards
d ​−3 (negative) = 3 red cards
We cancel out 3 black cards (positive) with 3 red cards (negative). We
are left with 1.
The equation 4 − 3 = 1 is the same as 4 + −3 = 1.
572 Unit 8 • Lesson 7
Lesson 7
How do we “add the opposite”?
Now that we know about positive and negative integers, we can think
of subtraction in a new way. We can think about it as “adding the
opposite.” When we subtract a positive integer, we replace the minus
sign with a plus sign and we rewrite the positive number as a negative.
Here are some examples:
Example 1
Show how to rewrite each subtraction problem as “adding the
opposite.”
4 − 3
4
Change the − to +
−
3
+
−3
=1
−9
= −2
−8
=0
7 − 9
Change the − to +
−
9
S
7
+
Change 9 to −9
8
4
Change 3 to −3
7
S
8 − 8
Change the − to +
−
8
S
8
+
Change 8 to −8
Changing subtraction problems into addition problems helps us think
about the relationship between the numbers in the problem.
Apply Skills
Turn to Interactive Text,
page 295.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 8 • Lesson 7 573
Lesson 7
Homework
Activity 1
Rewrite the subtraction problems as addition by adding the opposite.
1. 4 − 3 ​
2. −7 − 8 ​
3. 10 − 2 ​
4. −1 − 2 ​
5. 4 −4 ​
6. −11 − 7 ​
Activity 2
Solve the addition problems with positive and negative numbers.
1. 5 + −3
2. −4 + −7
3. −3 + 9
4. −7 + −2
5. 2 + −8
6. −4 + 14
7. −9 + 10
8. −3 + 3
9. 1 + −3
10. 5 + −2
Activity 3
Use the five cards in each of the problems to play the No Subtraction! Game.
Use as many cards as possible. Remember that the ace is 1 and the king,
queen and jack are 10.
1. You are dealt a 3, 4, 7, ace, and king. The goal number is 5.
2. You are dealt a queen, 2, 5, 6, and jack. The goal number is 10.
3. You are dealt an 8, 9, ace, 9, and jack. The goal number is 7.
Activity 4 • Distributed Practice
Solve.
1
2. Write 29% as a fraction. ​
3. Write 1.25 as a percent. ​
4. 12.28 − 14.99 ​
5. 1.68 ÷ 0.8 ​
6. 9 ÷ 3 ​
4
2
1
7. 8 · 3 ​
3
574 29
100
1. What is 2 of 100? ​
Unit 8 • Lesson 7
8.
3
1
37
100
49
+ 100
​
43
50
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