Use Patterns to Divide
Using patterns to divide is a Grade 5 math skill in enVision Mathematics, Chapter 5: Use Models and Strategies to Divide Whole Numbers. The key property is that multiplying or dividing both the dividend and divisor by the same number leaves the quotient unchanged: a / b = (a x 10) / (b x 10). This pattern simplifies division of large numbers by reducing to a known basic fact.
Key Concepts
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: $$a \div b = (a \times 10) \div (b \times 10)$$.
Common Questions
What division pattern stays true when you multiply both numbers by the same factor?
When you multiply both the dividend and the divisor by the same nonzero number, the quotient stays the same. For example, 12/4 = 120/40 = 3.
How does this pattern help divide large numbers?
You can simplify a complex division by dividing both numbers by a common factor until you reach a basic fact you know.
What is 4,800 / 60 using patterns?
Divide both by 10: 480 / 6 = 80. So 4,800 / 60 = 80.
Where is using patterns to divide taught in enVision Grade 5?
Chapter 5: Use Models and Strategies to Divide Whole Numbers in enVision Mathematics, Grade 5.
Why does this pattern work?
It is based on the property that the ratio stays constant when you scale both parts equally, like simplifying an equivalent fraction.