Learn on PengiPengi Math (Grade 5)Chapter 2: Multi-Digit Multiplication and Division with Place Value

Lesson 4: Understanding Division as Finding a Missing Factor

In this Grade 5 Pengi Math lesson, students learn to interpret division as an unknown-factor problem, connecting division equations directly to multiplication. They practice using multiplication to verify quotients and apply place value reasoning to solve division problems accurately. This lesson is part of Chapter 2: Multi-Digit Multiplication and Division with Place Value.

Section 1

Relating Division to Finding a Missing Factor

Property

Solving a division problem, such as A÷B=?A \div B = ?, is the same as finding the unknown factor in the related multiplication equation, B×?=AB \times ? = A.
The quotient of the division is the unknown factor.

Examples

Section 2

Use Patterns to Divide

Property

When you multiply or divide both the dividend and the divisor by the same number (except zero), the quotient does not change. For multiples of 10, this pattern can be shown as:

a÷b=(a×10)÷(b×10)a \div b = (a \times 10) \div (b \times 10)

Examples

Book overview

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

Continue this chapter

Chapter 2: Multi-Digit Multiplication and Division with Place Value

  1. Lesson 1

    Lesson 1: Estimating Products Using Rounding and Compatible Numbers

  2. Lesson 2

    Lesson 2: Modeling Multiplication with Area Models and Partial Products

  3. Lesson 3

    Lesson 3: Connecting Partial Products to the Standard Algorithm

  4. Lesson 4Current

    Lesson 4: Understanding Division as Finding a Missing Factor

  5. Lesson 5

    Lesson 5: Dividing Multi-Digit Numbers Using Area Models and Partial Quotients

  6. Lesson 6

    Lesson 6: Applying Division Algorithms and Interpreting Remainders

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Relating Division to Finding a Missing Factor

Property

Solving a division problem, such as A÷B=?A \div B = ?, is the same as finding the unknown factor in the related multiplication equation, B×?=AB \times ? = A.
The quotient of the division is the unknown factor.

Examples

Section 2

Use Patterns to Divide

Property

When you multiply or divide both the dividend and the divisor by the same number (except zero), the quotient does not change. For multiples of 10, this pattern can be shown as:

a÷b=(a×10)÷(b×10)a \div b = (a \times 10) \div (b \times 10)

Examples

Book overview

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

Continue this chapter

Chapter 2: Multi-Digit Multiplication and Division with Place Value

  1. Lesson 1

    Lesson 1: Estimating Products Using Rounding and Compatible Numbers

  2. Lesson 2

    Lesson 2: Modeling Multiplication with Area Models and Partial Products

  3. Lesson 3

    Lesson 3: Connecting Partial Products to the Standard Algorithm

  4. Lesson 4Current

    Lesson 4: Understanding Division as Finding a Missing Factor

  5. Lesson 5

    Lesson 5: Dividing Multi-Digit Numbers Using Area Models and Partial Quotients

  6. Lesson 6

    Lesson 6: Applying Division Algorithms and Interpreting Remainders