Division with Two-Digit Answers and a Remainder
Grade 4 students learn division with two-digit answers and remainders in Saxon Math Intermediate 4 Chapter 7 using the four-step long division cycle: Divide, Multiply, Subtract, Bring Down. For 87 ÷ 5: divide 8 by 5 (once, with 3 left), multiply 1 × 5 = 5, subtract 8 − 5 = 3, bring down 7 to make 37; divide 37 by 5 (seven times, with 2 left), multiply 7 × 5 = 35, subtract 37 − 35 = 2. Final answer: 17 R 2. Careful subtraction at each step prevents cascading errors.
Key Concepts
New Concept The pencil and paper method we use for dividing has four steps: divide, multiply, subtract, and bring down.
Why it matters Long division is your first encounter with a powerful mathematical tool called an algorithm, a step by step procedure for calculations. Mastering this systematic process of breaking down problems is essential for tackling more complex topics like fractions, ratios, and algebraic equations.
What’s next Next, you'll apply this four step cycle to solve division problems that result in two digit answers and a remainder.
Common Questions
What are the four steps of long division?
Divide, Multiply, Subtract, Bring Down—repeated in a cycle. Divide the current portion of the dividend by the divisor. Multiply that result by the divisor. Subtract to find the remainder. Bring down the next digit and repeat.
How do you solve 87 ÷ 5 using long division?
Round 1: 5 goes into 8 once (1). Multiply: 1 × 5 = 5. Subtract: 8 − 5 = 3. Bring down 7 to get 37. Round 2: 5 goes into 37 seven times (7). Multiply: 7 × 5 = 35. Subtract: 37 − 35 = 2. No more digits. Answer: 17 R 2.
What happens when the number you bring down is still smaller than the divisor?
Write a 0 in the quotient for that position, then bring down the next digit to form a larger number. This placeholder zero ensures the answer digits are in the correct positions.
Why is careful subtraction especially important in long division?
A subtraction error in any step carries forward, making all subsequent steps incorrect. If you get the wrong remainder after subtracting, the number you bring down will be wrong, and every following step will produce errors.
How do you check a long division answer with a remainder?
Multiply the quotient by the divisor, then add the remainder. The result must equal the original dividend. For 87 ÷ 5 = 17 R 2: (17 × 5) + 2 = 85 + 2 = 87. Correct.
What is the difference between the quotient and the remainder in long division?
The quotient is the whole-number answer—how many complete times the divisor fits. The remainder is what is left over after all complete groups are made. Both are part of the full answer.