Base Ten Operations
GradesGrade 4Base Ten Operations2-Digit × 2-Digit Multiplication

2-Digit × 2-Digit Multiplication

🏛️ Base Ten Operations
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2-Digit × 2-Digit Multiplication

Multiply two 2-digit numbers using partial products or the standard algorithm!

When both factors have two digits, we break the problem into smaller parts using place value. Each digit in the bottom number multiplies every digit in the top number — giving us partial products that we add together at the end.

Standard algorithm for 34 × 27:

1Step 1: Multiply 34 × 7 (ones digit of 27) = 238
2Step 2: Write a 0 placeholder, then multiply 34 × 2 (tens digit, which is really 20) = 68, shifted = 680
3Step 3: Add the partial products: 238 + 680 = 918
4Answer: 34 × 27 = 918
34×27=(34×7)+(34×20)=238+680=91834 \times 27 = (34 \times 7) + (34 \times 20) = 238 + 680 = 918
📦Partial products method for 36 × 45
Split each number by place value:
36 = 30 + 6
45 = 40 + 5

30 × 40 = 1,200
30 × 5  =   150
 6 × 40 =   240
 6 × 5  =    30
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Total:    1,620

Standard Algorithm

Work digit by digit with carrying36 × 5 = 180; 36 × 40 = 1,440180 + 1,440 = 1,620Faster once mastered

Partial Products

Break each factor by place value30×40 + 30×5 + 6×40 + 6×5 = 1,620Shows WHY the algorithm works

Both methods give the same answer. Partial products build understanding; the algorithm builds speed.

Always estimate first! 34 × 27 ≈ 30 × 30 = 900. Our answer 918 is close — great check!

✏️ Try It!

What is 24 × 35?

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Remember This!

Remember the zero placeholder! When multiplying by the tens digit (e.g., 2 in 27, which represents 20), write a 0 in the ones column first to shift the partial product one place left.

Practice with CalcVerse
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