Multiplication and divisionGrades 4–5
2-digit by 2-digit multiplication worksheets
Stacked two-digit by two-digit multiplication problems with blank rows beneath each one for partial products. Change the digit counts, layout and number of problems, then print the sheet with an answer key.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
- Free, no sign-up
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Multiplying by two digits
Two-digit by two-digit multiplication is the first time a child must break one number into parts and combine several products. It builds on single-digit facts, so a student who still hesitates on 7 × 8 will struggle here for that reason rather than for lack of understanding of the method. If the tables need work, try the 9 times table or the 12 times table first.
This generator stacks each problem and leaves empty rows underneath for the partial products, as its instruction line says. It is aimed at grades 4 and 5.
Settings
- Operation. Multiplication is the preset.
- Digits in the first number / second number. Both are 2. You can set the first number up to 6 digits and the second up to 5. A first number of 3 digits and a second of 2 digits is a natural next step, and 2 by 1 is a gentle starting point. The generator always puts the longer number on top.
- Layout. Vertical (stacked) gives you working space: one blank row for each digit in the bottom number. Horizontal prints the problem on one line without working rows, which suits mental math or estimation only.
- Number of problems. From 6 to 40. The preset is 12, because each problem takes room.
- Include the answer key, which shows the final product.
Each factor has exactly the number of digits you ask for, so a 2-digit setting never produces a single-digit factor.
Worked example: 47 × 36
- Ones digit of the bottom number. 47 × 6. 7 × 6 = 42: write 2 and carry 4. 4 × 6 = 24, plus 4 is 28. So the first partial product is 282.
- Tens digit of the bottom number. 47 × 30 (that is, 47 × 3, shifted one place). 7 × 3 = 21 and 4 × 3 = 12, so 47 × 3 = 141, and with the shift it is 1,410.
- Add the partial products. 282 + 1,410 = 1,692.
- Estimate. 50 × 36 = 1,800, and 47 is 3 less than 50, so subtract 3 × 36 = 108: 1,800 − 108 = 1,692. It agrees.
Students who forget the place-value shift often write 141 instead of 1,410. A zero placeholder in the ones column of the second row helps.
Reading the answer key
- Missing placeholder zero. The product is far too small, off by a factor of ten in the second row.
- Forgotten carry. One partial product is off by a small amount, often a single digit. Redo only that row.
- Fact errors. If the answer is wrong only in one digit, look for a basic fact slip such as 7 × 6 = 36.
- Adding errors at the end. The partial products are right but the sum is not. Re-add them.
- Misaligned columns. Squared paper keeps rows straight.
Mark each partial product separately so the student sees which step went wrong, and have them try the estimate every time. When this routine is fluent, long division is the natural inverse to check against.