Learn on PengiSaxon Math, Course 2Chapter 7: Lessons 61-70, Investigation 7

Lesson 64: Adding Positive and Negative Numbers

New Concept This course expands your understanding of numbers beyond simple counting. We will explore positive and negative numbers, fractions, and decimals to build a complete mathematical foundation. What’s next To begin, we'll focus on the rules for adding positive and negative numbers. Next, you’ll tackle worked examples with integers, fractions, and real world scenarios.

Section 1

📘 Adding Positive and Negative Numbers

New Concept

This course expands your understanding of numbers beyond simple counting. We will explore positive and negative numbers, fractions, and decimals to build a complete mathematical foundation.

What’s next

To begin, we'll focus on the rules for adding positive and negative numbers. Next, you’ll tackle worked examples with integers, fractions, and real-world scenarios.

Section 2

The sum of two numbers with the same sign

Property

The sum of two numbers with the same sign has an absolute value equal to the sum of their absolute values. Its sign is the same as the sign of the numbers.

Examples

(54)+(78)=132(-54) + (-78) = -132

(+20)+(+15)=+35(+20) + (+15) = +35

Section 3

The sum of two numbers with opposite signs

Property

The sum of two numbers with opposite signs has an absolute value equal to the difference of their absolute values. Its sign is the same as the sign of the number with the greater absolute value.

Examples

(+45)+(67)=22(+45) + (-67) = -22

(34)+(+43)=+9(-34) + (+43) = +9

Section 4

The sum of two opposites is zero

Property

The sum of two opposites is zero. For any number aa, this rule can be written as a+(a)=0a + (-a) = 0.

Examples

(92)+(+92)=0(-92) + (+92) = 0

(+3)+(3)=0(+3) + (-3) = 0

Book overview

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Chapter 7: Lessons 61-70, Investigation 7

  1. Lesson 1

    Lesson 61: Area of a Parallelogram, Angles of a Parallelogram

  2. Lesson 2

    Lesson 62: Classifying Triangles

  3. Lesson 3

    Lesson 63: Symbols of Inclusion

  4. Lesson 4Current

    Lesson 64: Adding Positive and Negative Numbers

  5. Lesson 5

    Lesson 65: Circumference and Pi

  6. Lesson 6

    Lesson 66: Ratio Problems Involving Totals

  7. Lesson 7

    Lesson 67: Geometric Solids

  8. Lesson 8

    Lesson 68: Algebraic Addition

  9. Lesson 9

    Lesson 69: Proper Form of Scientific Notation

  10. Lesson 10

    Lesson 70: Volume

  11. Lesson 11

    Investigation 7: Balanced Equations

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Adding Positive and Negative Numbers

New Concept

This course expands your understanding of numbers beyond simple counting. We will explore positive and negative numbers, fractions, and decimals to build a complete mathematical foundation.

What’s next

To begin, we'll focus on the rules for adding positive and negative numbers. Next, you’ll tackle worked examples with integers, fractions, and real-world scenarios.

Section 2

The sum of two numbers with the same sign

Property

The sum of two numbers with the same sign has an absolute value equal to the sum of their absolute values. Its sign is the same as the sign of the numbers.

Examples

(54)+(78)=132(-54) + (-78) = -132

(+20)+(+15)=+35(+20) + (+15) = +35

Section 3

The sum of two numbers with opposite signs

Property

The sum of two numbers with opposite signs has an absolute value equal to the difference of their absolute values. Its sign is the same as the sign of the number with the greater absolute value.

Examples

(+45)+(67)=22(+45) + (-67) = -22

(34)+(+43)=+9(-34) + (+43) = +9

Section 4

The sum of two opposites is zero

Property

The sum of two opposites is zero. For any number aa, this rule can be written as a+(a)=0a + (-a) = 0.

Examples

(92)+(+92)=0(-92) + (+92) = 0

(+3)+(3)=0(+3) + (-3) = 0

Book overview

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

Continue this chapter

Chapter 7: Lessons 61-70, Investigation 7

  1. Lesson 1

    Lesson 61: Area of a Parallelogram, Angles of a Parallelogram

  2. Lesson 2

    Lesson 62: Classifying Triangles

  3. Lesson 3

    Lesson 63: Symbols of Inclusion

  4. Lesson 4Current

    Lesson 64: Adding Positive and Negative Numbers

  5. Lesson 5

    Lesson 65: Circumference and Pi

  6. Lesson 6

    Lesson 66: Ratio Problems Involving Totals

  7. Lesson 7

    Lesson 67: Geometric Solids

  8. Lesson 8

    Lesson 68: Algebraic Addition

  9. Lesson 9

    Lesson 69: Proper Form of Scientific Notation

  10. Lesson 10

    Lesson 70: Volume

  11. Lesson 11

    Investigation 7: Balanced Equations