Multi-digit multiplication step by step: partial products vs the standard algorithm
How partial products and the standard algorithm work, why schools teach both, and worked examples you can follow with your child, one step at a time.
Skill guide · Grades 4–5
Multi-digit multiplication
How to multiply two-digit numbers with the standard algorithm and partial products, with a worked example and the mistakes to watch for.
What it is
Multi-digit multiplication means multiplying numbers with more than one digit, like 58 × 34. Most classes start with partial products (often drawn as a box or area model), then move to the standard algorithm, where each digit of the bottom number makes one line.
Fourth graders usually multiply up to four digits by one digit and two digits by two digits. Fifth graders use the standard algorithm for larger numbers.
A worked example
58 × 34 = 1972
1
2
2
3
5
8
×
3
4
2
3
2
×4
+
1
7
4
0
×3
1
9
7
2
Every step, the way the pad explains it
- Multiply 4 × 8 = 32. Write 2, carry 3.
- Multiply 4 × 5 = 20, plus the carried 3 = 23. Nothing left to multiply, so write the whole 23.
- Now multiply by the tens digit, 3. The placeholder 0 is already there. Multiply 3 × 8 = 24. Write 4, carry 2.
- Multiply 3 × 5 = 15, plus the carried 2 = 17. Nothing left to multiply, so write the whole 17.
- Add the ones: 2 + 0 = 2. Write 2.
- Add the tens: 3 + 4 = 7. Write 7.
- Add the hundreds: 2 + 7 = 9. Write 9.
- Add the thousands: only 1 here. Write 1.
- 1Multiply by the ones digit: 58 × 4 = 232. That is the first line.
- 2Write a 0 in the ones place of the second line, because the 3 means 30.
- 3Multiply by the tens digit: 58 × 3 = 174, written in front of the 0 to make 1740.
- 4Add the lines: 232 + 1740 = 1972.
- 5Estimate to check: about 60 × 30, which is 1800, so 1972 is reasonable.
Common mistakes
Leaving out the placeholder zero.
Say “the 3 is thirty” out loud before starting the second line.
Adding the carry before multiplying.
Multiply first, then add the carry.
Old carries from line one getting added into line two.
Cross out the first line’s carries before starting the second.
Slips in the final addition.
Treat it as a fresh addition problem, carrying and all.
Grade range and practice
Usually taught in grades 4–5. Schools order topics a little differently, so your child’s class may meet it earlier or later.
- Solve the same problem both ways, box and standard, and compare the lines.
- Start with two-digit by one-digit before moving to two-digit by two-digit.
- Keep a times table nearby until the facts are quick.
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