krit.club logo

Calculations - Multiplication of 4-digit numbers by 1-digit numbers

Grade 4IGCSE

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

🔑Concepts

•

Place Value: Identifying thousands (Th), hundreds (H), tens (T), and ones (O).

•

Standard Algorithm: Multiplying each digit of the 4-digit number by the 1-digit number starting from the right (ones).

•

Regrouping (Carrying): When the product of a column is 10 or greater, the tens digit is carried over to the next place value column.

•

Expanded Form: Breaking down the 4-digit number (e.g., 2435=2000+400+30+52435 = 2000 + 400 + 30 + 5) and multiplying each part separately.

•

Estimating: Rounding the 4-digit number to the nearest thousand to check the reasonableness of the final answer.

📐Formulae

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

a×(b+c+d+e)=(a×b)+(a×c)+(a×d)+(a×e)a \times (b + c + d + e) = (a \times b) + (a \times c) + (a \times d) + (a \times e) (Distributive Property)

💡Examples

Problem 1:

Calculate 1,212×41,212 \times 4.

Solution:

4,848

Explanation:

Multiply each digit by 4 starting from the ones: 4×2=84 \times 2 = 8 (ones), 4×1=44 \times 1 = 4 (tens), 4×2=84 \times 2 = 8 (hundreds), 4×1=44 \times 1 = 4 (thousands). No regrouping is required.

Problem 2:

Calculate 3,456×73,456 \times 7.

Solution:

24,192

Explanation:

Step 1: 7×6=427 \times 6 = 42. Write 2, carry 4. Step 2: 7×5=357 \times 5 = 35; 35+4=3935 + 4 = 39. Write 9, carry 3. Step 3: 7×4=287 \times 4 = 28; 28+3=3128 + 3 = 31. Write 1, carry 3. Step 4: 7×3=217 \times 3 = 21; 21+3=2421 + 3 = 24. Total is 24,192.

Problem 3:

A school buys 5 new laptops. Each laptop costs $1,850. What is the total cost?

Solution:

$9,250

Explanation:

Using the area model/expanded form: (5×1000)+(5×800)+(5×50)+(5×0)=5000+4000+250+0=9250(5 \times 1000) + (5 \times 800) + (5 \times 50) + (5 \times 0) = 5000 + 4000 + 250 + 0 = 9250.