Dividing 4-Digit Numbers
4A · Chapter 5 · Lesson 3 · MATH-4A-C05-L03
Learning goal. Divide four-digit values by appropriate one-digit divisors with exchanged place-value units.
Before you begin
Recall: Grade 3: single-digit division and remainder; 4A Ch4: multiplication estimates; Estimation and Division. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Is 818 ÷ 8 closer to 100 or 120?
Show answer & reasoning
Compare compatible products with 8; the quotient is near 102, which is closer to 100.
Estimate 602 ÷ 2 to the nearest ten in the quotient.
Show answer & reasoning
The exact quotient has whole-number part 301; rounding that to the nearest ten gives 300.
Estimate 415 ÷ 4 to the nearest ten in the quotient.
Show answer & reasoning
The exact quotient has whole-number part 103; rounding that to the nearest ten gives 100.
Key vocabulary
- dividend
- number being divided
- divisor
- number of equal groups or group size
- quotient
- result of division
- remainder
- amount left after complete groups
Understand the concept
Written four-digit division distributes thousands, hundreds, tens and ones into equal groups. When a place does not divide evenly, exchange the remainder into the next place, like turning leftover hundreds into tens. Keep zero digits in a quotient when a place receives no full unit. Always check divisor × quotient plus remainder.
Model it: place-value distribution chart and partial quotients. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Divide 8,892 by 9. Give the quotient and remainder.
8,892 = 9 × 988 + 0; the remainder 0 is less than 9.
Check your understanding 1
Divide 4,517 by 7. Give the quotient and remainder.
Show answer & reasoning
4,517 = 7 × 645 + 2; the remainder 2 is less than 7.
Worked example 2
Divide 3,160 by 4. Give the quotient and remainder.
3,160 = 4 × 790 + 0; the remainder 0 is less than 4.
Check your understanding 2
Divide 4,243 by 7. Give the quotient and remainder.
Show answer & reasoning
4,243 = 7 × 606 + 1; the remainder 1 is less than 7.
Worked example 3
Divide 5,786 by 7. Give the quotient and remainder.
5,786 = 7 × 826 + 4; the remainder 4 is less than 7.
Check your understanding 3
Divide 1,884 by 2. Give the quotient and remainder.
Show answer & reasoning
1,884 = 2 × 942 + 0; the remainder 0 is less than 2.
Guided practice
Divide 3,196 by 8. Give the quotient and remainder.
Show answer & reasoning
3,196 = 8 × 399 + 4; the remainder 4 is less than 8.
Divide 3,525 by 4. Give the quotient and remainder.
Show answer & reasoning
3,525 = 4 × 881 + 1; the remainder 1 is less than 4.
Divide 5,748 by 7. Give the quotient and remainder.
Show answer & reasoning
5,748 = 7 × 821 + 1; the remainder 1 is less than 7.
Divide 5,527 by 7. Give the quotient and remainder.
Show answer & reasoning
5,527 = 7 × 789 + 4; the remainder 4 is less than 7.
Divide 5,309 by 9. Give the quotient and remainder.
Show answer & reasoning
5,309 = 9 × 589 + 8; the remainder 8 is less than 9.
Independent practice
Divide 1,079 by 7. Give the quotient and remainder.
Show answer & reasoning
1,079 = 7 × 154 + 1; the remainder 1 is less than 7.
Divide 3,446 by 5. Give the quotient and remainder.
Show answer & reasoning
3,446 = 5 × 689 + 1; the remainder 1 is less than 5.
Divide 1,836 by 5. Give the quotient and remainder.
Show answer & reasoning
1,836 = 5 × 367 + 1; the remainder 1 is less than 5.
Divide 6,317 by 7. Give the quotient and remainder.
Show answer & reasoning
6,317 = 7 × 902 + 3; the remainder 3 is less than 7.
Divide 1,271 by 7. Give the quotient and remainder.
Show answer & reasoning
1,271 = 7 × 181 + 4; the remainder 4 is less than 7.
Divide 7,428 by 8. Give the quotient and remainder.
Show answer & reasoning
7,428 = 8 × 928 + 4; the remainder 4 is less than 8.
Divide 2,871 by 3. Give the quotient and remainder.
Show answer & reasoning
2,871 = 3 × 957 + 0; the remainder 0 is less than 3.
Divide 7,922 by 9. Give the quotient and remainder.
Show answer & reasoning
7,922 = 9 × 880 + 2; the remainder 2 is less than 9.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student claims 4,315 ÷ 7 equals 616 remainder 4. Check using multiplication, and correct the remainder.
Show answer & reasoning
7 × 616 = 4,312. To make 4,315, add remainder 3, which is less than 7.
Divide 4,868 by 7. Give the quotient and remainder.
Show answer & reasoning
4,868 = 7 × 695 + 3; the remainder 3 is less than 7.
Exit check
Divide 1,081 by 9. Give the quotient and remainder.
Show answer & reasoning
1,081 = 9 × 120 + 1; the remainder 1 is less than 9.
Divide 3,281 by 8. Give the quotient and remainder.
Show answer & reasoning
3,281 = 8 × 410 + 1; the remainder 1 is less than 8.
Divide 2,466 by 8. Give the quotient and remainder.
Show answer & reasoning
2,466 = 8 × 308 + 2; the remainder 2 is less than 8.