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Operations and Calculations - Multi-digit multiplication (long multiplication)

Grade 5IGCSE

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

🔑Concepts

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Place Value Alignment: Always align numbers vertically by their place value columns (ones, tens, hundreds).

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Partial Products: The process of multiplying the top number (multiplicand) by each individual digit of the bottom number (multiplier).

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Placeholder Zero: When multiplying by the tens digit, a '0' must be placed in the ones column. When multiplying by the hundreds digit, two zeros are used.

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Carrying (Regrouping): If a product of two digits is 10 or more, the tens digit is carried over to the next column and added after the next multiplication.

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Summation: The final step where all partial products are added together to find the total product.

📐Formulae

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

Partial Product 1+Partial Product 2+...=Total Product\text{Partial Product 1} + \text{Partial Product 2} + ... = \text{Total Product}

a×(b+c)=(a×b)+(a×c)a \times (b + c) = (a \times b) + (a \times c) (The Distributive Property used in decomposition)

💡Examples

Problem 1:

Calculate 43×2643 \times 26 using the long multiplication method.

Solution:

1,118

Explanation:

Step 1: Multiply 43 by 6 (ones place). 43×6=25843 \times 6 = 258. Step 2: Place a 0 in the ones column for the next row. Multiply 43 by 2 (tens place). 43×20=86043 \times 20 = 860. Step 3: Add the partial products: 258+860=1,118258 + 860 = 1,118.

Problem 2:

Find the product of 154154 and 3232.

Solution:

4,928

Explanation:

Step 1: Multiply 154×2=308154 \times 2 = 308. Step 2: Multiply 154×30154 \times 30. Write a 0 in the ones place, then 154×3=462154 \times 3 = 462, resulting in 4,620. Step 3: Add the partial products: 308+4,620=4,928308 + 4,620 = 4,928.

Problem 3:

A box contains 125 pens. How many pens are in 15 boxes?

Solution:

1,875

Explanation:

Multiply 125×15125 \times 15. First partial product (125×5125 \times 5) is 625. Second partial product (125×10125 \times 10) is 1,250. Adding 625+1,250625 + 1,250 gives a total of 1,875 pens.