Mental Division Using Multiplication Facts
This Grade 4 Eureka Math skill teaches students to solve division problems mentally by finding a quotient and remainder that satisfy (divisor times quotient) + remainder = dividend, where the remainder is less than the divisor. Students think in multiples of the divisor: for 27 divided by 4, the closest multiple not exceeding 27 is 4 times 6 = 24, giving quotient 6 and remainder 3. This mental division strategy from Chapter 13 of Eureka Math Grade 4 leverages multiplication fact fluency to efficiently compute division with remainders.
Key Concepts
To mentally solve a division problem, find a quotient ($q$) and a remainder ($r$) that satisfy the equation: $$(\text{divisor} \times q) + r = \text{dividend}$$ where the remainder is less than the divisor ($0 \leq r < \text{divisor}$).
Common Questions
How do you mentally solve a division problem?
Think of multiples of the divisor. Find the largest multiple that does not exceed the dividend. That multiple divided by the divisor is the quotient; the difference between the dividend and that multiple is the remainder.
How do you mentally solve 27 divided by 4?
Think: 4 times 6 = 24, which is the largest multiple of 4 not exceeding 27. Quotient = 6. Remainder = 27 minus 24 = 3. Answer: 6 R3.
How do you verify a mental division answer?
Check using (divisor times quotient) + remainder = dividend. For 6 R3 with divisor 4: (4 times 6) + 3 = 24 + 3 = 27. Correct.
What multiplication knowledge helps with mental division?
Knowing multiplication facts through 10 times 10 lets you quickly identify multiples of the divisor and find the closest one to the dividend without a calculator.
Can the remainder ever equal the divisor?
No. If the remainder equals the divisor, the quotient can be increased by 1 and the remainder becomes 0. The remainder must always be strictly less than the divisor.