Learn on PengiYoshiwara Elementary AlgebraChapter 2: Linear Equations

Lesson 1: Signed Numbers

In this Grade 6 lesson from Yoshiwara Elementary Algebra, Chapter 2, students learn to identify and work with signed numbers, including integers, positive and negative numbers, and their placement on a number line. Students practice using order symbols to compare negative numbers and apply rules for adding numbers with the same sign and opposite signs using absolute values. The lesson builds foundational skills for solving linear equations by developing fluency with signed number arithmetic.

Section 1

📘 Signed Numbers

New Concept

Mastering signed numbers is key to algebra. This lesson teaches the rules for adding, subtracting, multiplying, and dividing positive and negative numbers, preparing you to solve more complex equations.

What’s next

You'll start by visualizing addition and subtraction on a number line, followed by practice cards on multiplication and division.

Section 2

Integers and Order Symbols

Property

The natural numbers, zero, and the negatives of the natural numbers are called the integers:

…−3,−2,−1,0,1,2,3⋯\ldots -3, -2, -1, 0, 1, 2, 3 \cdots

We use special symbols to indicate order:

Section 3

Rules for Adding Integers

Property

  1. To add two numbers with the same sign, add their absolute values. The sum has the same sign as the numbers.
  1. To add two numbers with opposite signs, subtract their absolute values. The sum has the same sign as the number with the larger absolute value.

Examples

  • To add two numbers with the same sign, like (−8)+(−5)(-8) + (-5), we add their absolute values 8+5=138+5=13 and keep the sign, so the sum is −13-13.

Section 4

Rules for Subtracting Integers

Property

To subtract bb from aa:

  1. Change the sign of bb.
  1. Change the subtraction to addition.

Section 5

Products of Signed Numbers

Property

  1. The product of two numbers with opposite signs is a negative number.
  1. The product of two numbers with the same sign is a positive number.

Examples

  • The product of two numbers with opposite signs is negative: 8(−3)=−248(-3) = -24.

Section 6

Quotients of Signed Numbers

Property

The quotient of two numbers with opposite signs is a negative number.
The quotient of two numbers with the same sign is a positive number.
If aa is any nonzero number, then

0a=0anda0 is undefined.\frac{0}{a} = 0 \quad \text{and} \quad \frac{a}{0} \text{ is undefined.}

Examples

  • The quotient of two numbers with the same sign is positive: −45−9=5\frac{-45}{-9} = 5.
  • The quotient of two numbers with opposite signs is negative: 32÷(−4)=−832 \div (-4) = -8.

Book overview

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Chapter 2: Linear Equations

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    Lesson 1: Signed Numbers

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    Lesson 2: Expressions and Equations

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  3. Lesson 3

    Lesson 3: Graphs of Linear Equations

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  4. Lesson 4

    Lesson 4: Linear Equations and Inequalities

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    Lesson 5: Like Terms

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Lesson overview

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Section 1

📘 Signed Numbers

New Concept

Mastering signed numbers is key to algebra. This lesson teaches the rules for adding, subtracting, multiplying, and dividing positive and negative numbers, preparing you to solve more complex equations.

What’s next

You'll start by visualizing addition and subtraction on a number line, followed by practice cards on multiplication and division.

Section 2

Integers and Order Symbols

Property

The natural numbers, zero, and the negatives of the natural numbers are called the integers:

…−3,−2,−1,0,1,2,3⋯\ldots -3, -2, -1, 0, 1, 2, 3 \cdots

We use special symbols to indicate order:

Section 3

Rules for Adding Integers

Property

  1. To add two numbers with the same sign, add their absolute values. The sum has the same sign as the numbers.
  1. To add two numbers with opposite signs, subtract their absolute values. The sum has the same sign as the number with the larger absolute value.

Examples

  • To add two numbers with the same sign, like (−8)+(−5)(-8) + (-5), we add their absolute values 8+5=138+5=13 and keep the sign, so the sum is −13-13.

Section 4

Rules for Subtracting Integers

Property

To subtract bb from aa:

  1. Change the sign of bb.
  1. Change the subtraction to addition.

Section 5

Products of Signed Numbers

Property

  1. The product of two numbers with opposite signs is a negative number.
  1. The product of two numbers with the same sign is a positive number.

Examples

  • The product of two numbers with opposite signs is negative: 8(−3)=−248(-3) = -24.

Section 6

Quotients of Signed Numbers

Property

The quotient of two numbers with opposite signs is a negative number.
The quotient of two numbers with the same sign is a positive number.
If aa is any nonzero number, then

0a=0anda0 is undefined.\frac{0}{a} = 0 \quad \text{and} \quad \frac{a}{0} \text{ is undefined.}

Examples

  • The quotient of two numbers with the same sign is positive: −45−9=5\frac{-45}{-9} = 5.
  • The quotient of two numbers with opposite signs is negative: 32÷(−4)=−832 \div (-4) = -8.

Book overview

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

Continue this chapter

Chapter 2: Linear Equations

  1. Lesson 1Current

    Lesson 1: Signed Numbers

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  2. Lesson 2

    Lesson 2: Expressions and Equations

    LearnPractice
  3. Lesson 3

    Lesson 3: Graphs of Linear Equations

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  4. Lesson 4

    Lesson 4: Linear Equations and Inequalities

    LearnPractice
  5. Lesson 5

    Lesson 5: Like Terms

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