Representing Comparison with Division and Multiplication
Representing Comparison with Division and Multiplication is a Grade 3 math skill from Eureka Math showing how a division problem can be rewritten as a multiplication problem with an unknown factor. The equation a ÷ b = ? is equivalent to ? × b = a. For example, 24 ÷ 6 = ? becomes ? × 6 = 24. This flexibility lets students use known multiplication facts to solve division problems quickly, reinforcing the inverse relationship between the two operations and building algebraic thinking.
Key Concepts
A division problem can be rewritten as a multiplication problem with an unknown factor. The unknown factor is the answer to the division problem. $$a \div b = ? \quad \text{is the same as} \quad ? \times b = a$$.
Common Questions
How can a division problem be rewritten as multiplication?
a ÷ b = ? is the same as ? × b = a. The unknown quotient becomes the unknown factor in a multiplication equation.
How would you rewrite 35 ÷ 7 = ? as multiplication?
? × 7 = 35. Since 5 × 7 = 35, the answer is 5. This uses known multiplication facts to solve division.
Why is it useful to think of division as finding an unknown factor?
Students typically learn multiplication facts first. Rewriting division as multiplication lets them use those memorized facts to solve division problems without a separate procedure.
What is the inverse relationship between multiplication and division?
Multiplication and division are opposite operations. If a × b = c, then c ÷ a = b and c ÷ b = a. They undo each other.
In which textbook is Representing Comparison with Division and Multiplication taught?
This skill is taught in Eureka Math, Grade 3.