Multi-Digit Multiplication and Division: Grade 4 Study Guide
Grade 4 moves from single-digit facts to multi-digit calculations, using place value to explain every step.
In Grade 4, children multiply a number of up to four digits by a one-digit number, and multiply two two-digit numbers. They also divide numbers of up to four digits by a one-digit number, with remainders. The standards ask for methods based on place value, the properties of operations and models such as area models, not only a memorized procedure.
Fluent multiplication facts to 10 × 10 are the base. Without them, long calculations become slow and error-prone, so a few minutes of fact practice each day pays off for the whole year.
The area model for multiplication
Break each number into tens and ones, draw a rectangle and find the area of each part. For 23 × 14, split into (20 + 3) × (10 + 4). The four partial products are 20 × 10 = 200, 20 × 4 = 80, 3 × 10 = 30 and 3 × 4 = 12. Add them: 200 + 80 + 30 + 12 = 322.
| 10 | 4 | |
|---|---|---|
| 20 | 200 | 80 |
| 3 | 30 | 12 |
Standard algorithm for multiplication
The standard method records the same partial products in a shorter form. Multiply by the ones digit first, then by the tens digit (writing a zero as a placeholder), then add.
Multiply the ones: 6 × 3 = 18. Write 8, carry 1.
4 × 3 = 12, plus the carried 1 is 13.
138.
46 is about 50, and 50 × 3 = 150, so 138 is sensible.
Division with remainders
Division asks how many equal groups fit, or how many are in each group. Use the relationship dividend = divisor × quotient + remainder. For 157 ÷ 4: 4 goes into 15 three times (12), leaving 3. Bring down the 7 to make 37. 4 goes into 37 nine times (36), leaving 1. So 157 ÷ 4 = 39 remainder 1. Check: 4 × 39 + 1 = 157.
| Step | Work | Result |
|---|---|---|
| Divide | 15 ÷ 4 | 3 (tens place) |
| Multiply and subtract | 15 − 12 | 3 |
| Bring down 7 | 37 ÷ 4 | 9 (ones place) |
| Remainder | 37 − 36 | 1 |
Worked examples and common mistakes
Example: A school buys 12 boxes of 36 pencils. 12 × 36 = 360 + 72 = 432 pencils. Example: 250 cookies are shared among 6 classes. 250 ÷ 6 = 41 remainder 4, so each class gets 41 and 4 are left over. Common mistakes: forgetting the placeholder zero in the second row, losing a carried digit, and ignoring what a remainder means in the story. Sometimes you round up (buses needed), sometimes you drop it (full bags).
Check your understanding: model answers
1. 34 × 25 = 680 + 170 = 850. 2. 408 ÷ 6 = 68. 3. 250 ÷ 48 = 5 remainder 10, so 6 buses are needed.
✨ Key Takeaways
- Use place value and area models to multiply.
- The standard algorithm records the same partial products.
- Division: dividend = divisor × quotient + remainder.
- Always estimate and check.
💬 Questions for Discussion & Reflection
- Find 34 × 25.
- Find 408 ÷ 6.
- A bus holds 48 students. How many buses for 250 students?
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