Learn on PengiPengi Math (Grade 7)Chapter 2: Rational Numbers and Exponents

Lesson 3: Multiplying and Dividing Rational Numbers

In this Grade 7 Pengi Math lesson from Chapter 2: Rational Numbers and Exponents, students learn to multiply and divide fractions and decimals with positive and negative signs, including the correct placement of negative signs in fractions. The lesson also covers simplifying complex fractions and evaluating algebraic expressions that involve rational numbers.

Section 1

Multiplying Different Forms of Rational Numbers

Property

To multiply rational numbers in different forms, such as a decimal and a fraction, first convert them to a common form. You can either convert the decimal to a fraction or the fraction to a decimal before multiplying.

Examples

Section 2

Dividing Rational Numbers in Different Forms

Property

To divide rational numbers that are in different forms, first convert them to the same form (usually fractions) and then divide.

  • If the signs are the same (both positive or both negative), the quotient is positive
  • If the signs are different (one positive, one negative), the quotient is negative

Examples

Section 3

Placement of the Negative Sign in Division

Property

For any integers aa and bb (with b≠0b \neq 0):

−ab=−ab=a−b-\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b}

Examples

Book overview

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Chapter 2: Rational Numbers and Exponents

  1. Lesson 1

    Lesson 1: Rational Numbers and Decimal Expansion

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  2. Lesson 2

    Lesson 2: Adding and Subtracting Rational Numbers

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  3. Lesson 3Current

    Lesson 3: Multiplying and Dividing Rational Numbers

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  4. Lesson 4

    Lesson 4: Introduction to Roots and Estimation

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  5. Lesson 5

    Lesson 5: Exponents and Order of Operations

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Lesson overview

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Section 1

Multiplying Different Forms of Rational Numbers

Property

To multiply rational numbers in different forms, such as a decimal and a fraction, first convert them to a common form. You can either convert the decimal to a fraction or the fraction to a decimal before multiplying.

Examples

Section 2

Dividing Rational Numbers in Different Forms

Property

To divide rational numbers that are in different forms, first convert them to the same form (usually fractions) and then divide.

  • If the signs are the same (both positive or both negative), the quotient is positive
  • If the signs are different (one positive, one negative), the quotient is negative

Examples

Section 3

Placement of the Negative Sign in Division

Property

For any integers aa and bb (with b≠0b \neq 0):

−ab=−ab=a−b-\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b}

Examples

Book overview

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

Continue this chapter

Chapter 2: Rational Numbers and Exponents

  1. Lesson 1

    Lesson 1: Rational Numbers and Decimal Expansion

    LearnPractice
  2. Lesson 2

    Lesson 2: Adding and Subtracting Rational Numbers

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Multiplying and Dividing Rational Numbers

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  4. Lesson 4

    Lesson 4: Introduction to Roots and Estimation

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  5. Lesson 5

    Lesson 5: Exponents and Order of Operations

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