Equivalent Division Problems
Equivalent division problems use the property that multiplying or dividing both the dividend and divisor by the same number produces the same quotient in Grade 6 math (Saxon Math, Course 1). For example, 50 ÷ 10 = 5/1 = 5; and 100 ÷ 20 = 5 (both multiplied by 2). This is the same as simplifying a fraction: 50/10 = 5/1. This technique simplifies messy division: 4.5 ÷ 0.3 becomes 45 ÷ 3 = 15 (multiply both by 10). It is also useful for mental math: 240 ÷ 8 = 30 ÷ 1 = 30 (divide both by 8). Recognizing equivalent division problems is key for dividing decimals and for understanding ratio equivalence.
Key Concepts
New Concept You can create an equivalent division problem by multiplying or dividing the dividend and divisor by the same number. This simplifies the problem, just like reducing a fraction. What’s next Next, we'll review worked examples showing how to simplify division with whole numbers and fractions, and also solve for unknowns in equations.
Common Questions
What makes two division problems equivalent?
Multiplying or dividing both the dividend and divisor by the same nonzero number gives an equivalent division with the same quotient.
How does 4.5 ÷ 0.3 become a simpler problem?
Multiply both by 10: 45 ÷ 3 = 15. The decimal is eliminated without changing the answer.
How is simplifying a fraction the same as creating an equivalent division?
A fraction a/b is a ÷ b. Dividing both by their GCF produces the same value in simpler form: 50/10 = 5/1 = 5.
How do you use equivalent division for mental math with 240 ÷ 8?
Divide both by 8: 30 ÷ 1 = 30. Or divide by 4 first: 60 ÷ 2 = 30.
Does this principle work with multiplication too?
No — multiplying both factors by the same number does change the product. This property is specific to division (and fraction equivalence).