Learn on PengienVision, Mathematics, Grade 5Chapter 5: Use Models and Strategies to Divide Whole Numbers

Lesson 1: Use Patterns and Mental Math to Divide

In this Grade 5 lesson from enVision Mathematics, students learn to use place value patterns and basic multiplication facts to mentally divide multiples of 10, such as finding quotients like 18,000 ÷ 90 by relating them to the basic fact 18 ÷ 9. The lesson covers dividing with multiples of 10 up to five-digit dividends and two-digit divisors using mental math strategies. It is part of Chapter 5, which focuses on models and strategies for dividing whole numbers.

Section 1

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

Section 2

Strategy: Divide Multiples of 10 by Multiples of 10

Property

To divide multiples of 10, you can simplify the problem by dividing both the dividend and the divisor by 10. This pattern allows you to use a basic division fact.

420÷60=(420÷10)÷(60÷10)=42÷6420 \div 60 = (420 \div 10) \div (60 \div 10) = 42 \div 6

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

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

Section 2

Strategy: Divide Multiples of 10 by Multiples of 10

Property

To divide multiples of 10, you can simplify the problem by dividing both the dividend and the divisor by 10. This pattern allows you to use a basic division fact.

420÷60=(420÷10)÷(60÷10)=42÷6420 \div 60 = (420 \div 10) \div (60 \div 10) = 42 \div 6

Examples