Learn on PengiBig Ideas Math, Course 2Chapter 1: Integers

Lesson 3: Subtracting Integers

In this Grade 7 lesson from Big Ideas Math, Course 2, students learn how to subtract integers by applying the rule of adding the opposite, expressed as a - b = a + (-b). The lesson covers subtracting positive and negative integers, evaluating multi-term integer expressions, and solving real-life problems such as finding ranges of elevation using integer subtraction.

Section 1

Subtracting a Positive Number

Property

Subtracting a positive number is the same as adding the corresponding negative number. For both operations, we move to the left on the number line.

Examples

  • To solve 7−(+12)7 - (+12), we change it to an addition problem: 7+(−12)=−57 + (-12) = -5.
  • To solve −5−(+6)-5 - (+6), we rewrite it as adding a negative: −5+(−6)=−11-5 + (-6) = -11.
  • The subtraction 15−(+8)15 - (+8) is the same as the addition 15+(−8)15 + (-8), which equals 77.

Explanation

Think of subtracting a positive number as taking away value. This makes you move left on the number line, which is exactly what happens when you add a negative number. It's two ways of describing the same decrease.

Section 2

Subtracting negative integers on number line

Property

Subtracting a negative number gives the same result as adding a positive number. For both operations, we move to the right on the number line.

Examples

  • The problem 4−(−9)4 - (-9) becomes an addition problem. We solve 4+(+9)4 + (+9) to get 1313.
  • For −10−(−3)-10 - (-3), we change it to −10+(+3)-10 + (+3), which gives us an answer of −7-7.
  • Subtracting a negative from a negative, as in −6−(−11)-6 - (-11), is the same as −6+11-6 + 11, which equals 55.

Explanation

Imagine someone cancels a debt you owe. Taking away that negative debt increases your net worth! Similarly, subtracting a negative number is like adding a positive one, causing you to move right on the number line.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Subtracting a Positive Number

Property

Subtracting a positive number is the same as adding the corresponding negative number. For both operations, we move to the left on the number line.

Examples

  • To solve 7−(+12)7 - (+12), we change it to an addition problem: 7+(−12)=−57 + (-12) = -5.
  • To solve −5−(+6)-5 - (+6), we rewrite it as adding a negative: −5+(−6)=−11-5 + (-6) = -11.
  • The subtraction 15−(+8)15 - (+8) is the same as the addition 15+(−8)15 + (-8), which equals 77.

Explanation

Think of subtracting a positive number as taking away value. This makes you move left on the number line, which is exactly what happens when you add a negative number. It's two ways of describing the same decrease.

Section 2

Subtracting negative integers on number line

Property

Subtracting a negative number gives the same result as adding a positive number. For both operations, we move to the right on the number line.

Examples

  • The problem 4−(−9)4 - (-9) becomes an addition problem. We solve 4+(+9)4 + (+9) to get 1313.
  • For −10−(−3)-10 - (-3), we change it to −10+(+3)-10 + (+3), which gives us an answer of −7-7.
  • Subtracting a negative from a negative, as in −6−(−11)-6 - (-11), is the same as −6+11-6 + 11, which equals 55.

Explanation

Imagine someone cancels a debt you owe. Taking away that negative debt increases your net worth! Similarly, subtracting a negative number is like adding a positive one, causing you to move right on the number line.