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Multiplication - Multiplication of 3-digit by 1-digit Number

Grade 3ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Identifying the Components: In a multiplication sum, the 3-digit number being multiplied is called the Multiplicand, and the 1-digit number we multiply by is the Multiplier. When written vertically, the Multiplicand sits on top and the Multiplier sits below it, aligned to the right.

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Vertical Alignment and Place Value: To solve the problem correctly, align the 1-digit multiplier directly under the ones place of the 3-digit number. Visualize three columns labeled H (Hundreds), T (Tens), and O (Ones); the multiplier must stay in the 'O' column to ensure correct place value calculation.

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The Right-to-Left Rule: Multiplication always begins from the rightmost digit and moves to the left. You multiply the multiplier by the ones digit first, then the tens digit, and finally the hundreds digit.

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Regrouping (Carrying Over): If the product in any column is 1010 or greater (for example, 8×2=168 \times 2 = 16), write the ones digit (66) in the answer row and 'carry' the tens digit (11) to the top of the next column on the left. This small carried number is added to the result of the next multiplication step.

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Handling Zero in Multiplicand: When a 3-digit number contains a zero (e.g., 204×2204 \times 2), any digit multiplied by 00 is 00. However, if there is a carried-over number from the previous column, you must add it to this zero result before writing the answer for that column.

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The Expanded Form Method: You can visualize a 3-digit multiplication by breaking the number into parts. For example, 234×2234 \times 2 can be seen as (200×2)+(30×2)+(4×2)(200 \times 2) + (30 \times 2) + (4 \times 2). This helps in understanding how each place value contributes to the final product.

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The Identity Property: Any 3-digit number multiplied by 11 remains the same. Visually, the product row will look exactly like the multiplicand row, as H×1H \times 1, T×1T \times 1, and O×1O \times 1 do not change the values.

📐Formulae

Multiplicand×Multiplier=Product\text{Multiplicand} \times \text{Multiplier} = \text{Product}

Expanded Form: (H+T+O)×m=(H×m)+(T×m)+(O×m)\text{Expanded Form: } (H + T + O) \times m = (H \times m) + (T \times m) + (O \times m)

Regrouping Rule: If O×m≥10, then Tens digit is carried to T column\text{Regrouping Rule: If } O \times m \ge 10, \text{ then } \text{Tens digit is carried to T column}

💡Examples

Problem 1:

Multiply 123123 by 33.

Solution:

123×3=369123 \times 3 = 369

  1. Multiply the ones: 3×3=93 \times 3 = 9. Write 99 in the ones place.
  2. Multiply the tens: 2×3=62 \times 3 = 6. Write 66 in the tens place.
  3. Multiply the hundreds: 1×3=31 \times 3 = 3. Write 33 in the hundreds place.

Explanation:

This is a multiplication problem without regrouping. We simply multiply each digit of the 3-digit number by the 1-digit multiplier from right to left.

Problem 2:

Find the product of 246246 and 44.

Solution:

246×4=984246 \times 4 = 984

  1. Ones: 6×4=246 \times 4 = 24. Write 44 in the ones place and carry 22 to the tens place.
  2. Tens: 4×4=164 \times 4 = 16. Add the carried 22: 16+2=1816 + 2 = 18. Write 88 in the tens place and carry 11 to the hundreds place.
  3. Hundreds: 2×4=82 \times 4 = 8. Add the carried 11: 8+1=98 + 1 = 9. Write 99 in the hundreds place.

Explanation:

This example demonstrates regrouping (carrying). When a product exceeds 99, the tens digit of that product must be added to the result of the next column's multiplication.