Learn on PengiBig Ideas Math, Advanced 1Chapter 11: Integers

Lesson 3: Subtracting Integers

In this Grade 6 lesson from Big Ideas Math Advanced 1, Chapter 11, students learn to subtract integers by applying the rule of adding the opposite, converting expressions like −8 − (−13) into −8 + 13. Students practice subtracting positive and negative integers, evaluate multi-term expressions, and apply integer subtraction to real-life problems such as calculating ranges of elevation.

Section 1

Subtracting Negative Integers on a Number Line

Property

When subtracting a negative integer on a number line, move right (in the positive direction) by the absolute value of that negative integer: a(b)=a+ba - (-b) = a + b.

Examples

Section 2

Subtraction as Adding the Opposite

Property

Subtraction of integers is the same as adding the additive inverse, so pq=p+(q)p - q = p + (-q). A number and its opposite have a sum of 0 and are called additive inverses. The opposite of aa is written as a-a.

Examples

Section 3

Applying the Rule for Subtracting Integers

Property

Apply the rule that subtraction of integers is equivalent to adding the opposite: ab=a+(b)a - b = a + (-b). This allows any integer subtraction problem to be solved using addition rules, including cases with negative integers where a(b)=a+ba - (-b) = a + b.

Examples

Book overview

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Chapter 11: Integers

  1. Lesson 1

    Lesson 1: Integers and Absolute Value

  2. Lesson 2

    Lesson 2: Adding Integers

  3. Lesson 3Current

    Lesson 3: Subtracting Integers

  4. Lesson 4

    Lesson 4: Multiplying Integers

  5. Lesson 5

    Lesson 5: Dividing Integers

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Subtracting Negative Integers on a Number Line

Property

When subtracting a negative integer on a number line, move right (in the positive direction) by the absolute value of that negative integer: a(b)=a+ba - (-b) = a + b.

Examples

Section 2

Subtraction as Adding the Opposite

Property

Subtraction of integers is the same as adding the additive inverse, so pq=p+(q)p - q = p + (-q). A number and its opposite have a sum of 0 and are called additive inverses. The opposite of aa is written as a-a.

Examples

Section 3

Applying the Rule for Subtracting Integers

Property

Apply the rule that subtraction of integers is equivalent to adding the opposite: ab=a+(b)a - b = a + (-b). This allows any integer subtraction problem to be solved using addition rules, including cases with negative integers where a(b)=a+ba - (-b) = a + b.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 11: Integers

  1. Lesson 1

    Lesson 1: Integers and Absolute Value

  2. Lesson 2

    Lesson 2: Adding Integers

  3. Lesson 3Current

    Lesson 3: Subtracting Integers

  4. Lesson 4

    Lesson 4: Multiplying Integers

  5. Lesson 5

    Lesson 5: Dividing Integers