Equivalent Division Problems
Equivalent division problems is a Grade 6 math skill in Saxon Math, Course 1, Chapter 5 that teaches students to simplify division by multiplying or dividing both the dividend and divisor by the same number—just like reducing a fraction. For example, 700 ÷ 14 simplifies to 350 ÷ 7 = 50 by dividing both numbers by 2. This technique eliminates decimals and large numbers: 5.6 ÷ 0.7 becomes 56 ÷ 7 = 8 by multiplying both by 10. The rule is identical to the property of fractions: changing both terms by the same factor preserves the quotient. One critical caution: the operation must be applied to both numbers, not just one.
Key Concepts
Property Two division problems that have the same quotient are called equivalent division problems. You can create one by multiplying or dividing both the dividend and the divisor by the same number. $$ \frac{700}{14} = \frac{350}{7} $$.
Examples Example: Simplify by dividing both numbers by 4: $1200 \div 16 \rightarrow (1200 \div 4) \div (16 \div 4) = 300 \div 4 = 75$. Example: Simplify by doubling both numbers to remove fractions: $7\frac{1}{2} \div 2\frac{1}{2} \rightarrow (7\frac{1}{2} \cdot 2) \div (2\frac{1}{2} \cdot 2) = 15 \div 5 = 3$. Example: Simplify by multiplying by 10 to remove decimals: $6.4 \div 0.8 \rightarrow (6.4 \cdot 10) \div (0.8 \cdot 10) = 64 \div 8 = 8$.
Explanation Tired of dividing by tricky numbers? You can simplify a division problem by multiplying or dividing both the dividend and the divisor by the same number. It's just like reducing a fraction, but for division! This trick makes mental math a breeze by turning complex problems into much simpler ones.
Common Questions
What makes two division problems equivalent?
Two division problems are equivalent when they produce the same quotient. You create one by multiplying or dividing both the dividend and divisor by the same number, just like simplifying a fraction.
How do you use equivalent division to remove decimals?
Multiply both numbers by a power of 10 to shift the decimal point. For 5.6 ÷ 0.7, multiply both by 10 to get 56 ÷ 7 = 8.
Can you use equivalent division to simplify large numbers?
Yes. For 1200 ÷ 16, divide both by 4 to get 300 ÷ 4 = 75. Choosing a common factor of both numbers simplifies the calculation.
What is the most common mistake with equivalent division?
Changing only one number in the problem. You must apply the same multiplication or division to both the dividend and the divisor, or the quotient will change.
How is equivalent division related to fraction simplification?
Division a ÷ b is the same as the fraction a/b. Simplifying a/b by dividing numerator and denominator by the same factor is identical to creating an equivalent division problem.