Learn on PengiReveal Math, AcceleratedUnit 5: Solve Problems Involving Operations with Integers and Rational Numbers

Lesson 5-3: Subtract Integers and Rational Numbers

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to subtract integers and rational numbers by applying the additive inverse property, rewriting expressions like p − q as p + (−q). Students also use number lines to visualize subtraction and calculate the distance between two values using absolute value. Real-world contexts, including temperature ranges on Mars and competition point totals, give students practice applying these skills across Unit 5.

Section 1

Subtracting Integers on a Number Line

Property

To model the subtraction problem a−ba - b on a number line, start at the point representing the first integer, aa. Then, move a distance of ∣b∣|b| units. Move to the left if bb is positive, and move to the right if bb is negative.

Examples

  • To find 3−53 - 5: Start at 33 and move 55 units to the left. You land on −2-2. So, 3−5=−23 - 5 = -2.
  • To find −2−4-2 - 4: Start at −2-2 and move 44 units to the left. You land on −6-6. So, −2−4=−6-2 - 4 = -6.
  • To find 1−(−4)1 - (-4): Start at 11 and move 44 units to the right. You land on 55. So, 1−(−4)=51 - (-4) = 5.

Explanation

A number line provides a visual way to understand integer subtraction. You always begin at the first number in the expression. Subtracting a positive integer is like a decrease, so you move to the left. Subtracting a negative integer is equivalent to adding its positive opposite, so you move to the right. The final position on the number line represents the answer to the subtraction problem.

Section 2

Subtraction Property

Property

a−b=a+(−b)a - b = a + (-b)

Subtracting a number is the same as adding its opposite.

Examples

  • The expression 14−814 - 8 can be rewritten as adding the opposite: 14+(−8)14 + (-8), which both equal 66.

Section 3

Subtraction of a Negative Number

Property

When subtracting a negative number, the result equals adding the positive version of that number:

x−(−y)=x+yx - (-y) = x + y

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Subtracting Integers on a Number Line

Property

To model the subtraction problem a−ba - b on a number line, start at the point representing the first integer, aa. Then, move a distance of ∣b∣|b| units. Move to the left if bb is positive, and move to the right if bb is negative.

Examples

  • To find 3−53 - 5: Start at 33 and move 55 units to the left. You land on −2-2. So, 3−5=−23 - 5 = -2.
  • To find −2−4-2 - 4: Start at −2-2 and move 44 units to the left. You land on −6-6. So, −2−4=−6-2 - 4 = -6.
  • To find 1−(−4)1 - (-4): Start at 11 and move 44 units to the right. You land on 55. So, 1−(−4)=51 - (-4) = 5.

Explanation

A number line provides a visual way to understand integer subtraction. You always begin at the first number in the expression. Subtracting a positive integer is like a decrease, so you move to the left. Subtracting a negative integer is equivalent to adding its positive opposite, so you move to the right. The final position on the number line represents the answer to the subtraction problem.

Section 2

Subtraction Property

Property

a−b=a+(−b)a - b = a + (-b)

Subtracting a number is the same as adding its opposite.

Examples

  • The expression 14−814 - 8 can be rewritten as adding the opposite: 14+(−8)14 + (-8), which both equal 66.

Section 3

Subtraction of a Negative Number

Property

When subtracting a negative number, the result equals adding the positive version of that number:

x−(−y)=x+yx - (-y) = x + y

Examples