Understanding Subtraction of Integers and Other Rational Numbers

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Solution, examples, and videos to help Grade 7 students learn how to understand subtraction of integers and other rational numbers.

New York State Common Core Math Grade 7, Module 2, Lesson 5.
Grade 7, Module 2, Lesson 5 Worksheets (pdf)

New York State Common Core Math Grade 7, Module 2, Lesson 5

The following figures show how to subtract integers using the rules. Scroll down the page for more examples and solutions.

Lesson 5 Student Outcomes

Students justify the rule for subtraction: Subtracting a number is the same as adding its opposite.

Students relate the rule for subtraction to the Integer Game: removing (subtracting) a positive card changes the score in the same way as adding a corresponding negative card. Removing (subtracting) a negative card makes the same change as adding the corresponding positive card.

Students justify the rule for subtraction for all rational numbers from the inverse relationship between addition and subtraction; i.e., subtracting a number and adding it back gets you back to where you started: (m - n) + n = m

Lesson 5 Summary

The Rule for Subtraction: Subtracting a number is the same as adding its opposite.

Removing (subtracting) a positive card changes the score in the same way as adding a corresponding negative card.

Removing (subtracting) a negative card makes the same change as adding the corresponding positive card.

For all rational numbers, subtracting a number and adding it back gets you back to where you started: (m - n) + n = m

Example 1: Exploring Subtraction with the Integer Game

Discussion: Making Connections to Integer Subtraction
1. How did selecting positive value cards change the value of your hand?
2. How did selecting negative value cards change the value of your hand?
3. How did discarding positive value cards change the value of your hand?
4. How did discarding negative value cards change the value of your hand?
5. What operation reflects selecting a card?
6. What operation reflects discarding or removing a card?
7. Based on the game, can you make a prediction about what happens to the result when:
a. Subtracting a positive integer.
b. Subtracting a negative integer.

Example 2: Subtracting a Positive Number

a. The teacher leads whole class by modeling an Integer Game example to find the sum of 4 and 2
b. Show that discarding (subtracting) a positive card, which is the same as subtracting a positive number, decreases the value of the hand.

Example 3: Subtracting a Negative Number

Follow along with the teacher, completing the diagrams below.
a. How does removing a negative card change the score, or value, of the hand?

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The Rule of Subtraction: Subtracting a number is the same as adding its additive inverse (or opposite).

Lesson 5 Exercises

Exercises 1–2: Subtracting Positive and Negative Integers

1. Using the rule of subtraction, rewrite the following subtraction sentences as addition sentences and solve. Use the number line below if needed.

a. 8 - 2
b. 4 - 9
c. -3 -7
d. -9 - (-2)

2. Find the differences.

a. -2 - (-5)
b. 11 - (-8)
c. -10 - (-4)

Lesson 5 Exercise

3. Write two equivalent expressions that would represent, “An airplane flies at an altitude of 25,000 feet. A submarine dives to depth of 600 feet below sea level. What is the difference in their elevations?”

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Lesson 5 Problem Set

2. You and your partner were playing the Integer Game in class. Here are the cards in both hands.
a. Find the value of each hand. Who would win based on the current scores? (The score closest to wins.)
b. Find the value of each hand if you discarded the -2 and selected a 5, and your partner discarded the -5 and selected a 5. Show your work to support your answer.
c. Use your score values from part (b) to determine who would win the game now.

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