Multiplication
Definition: Multiplication is a mathematical operation in which a number (the multiplicand) is added to itself a number of times specified by another number (the multiplier). The result of multiplication is called the product.
Multiplication is commutative, meaning the order of the numbers does not matter: \[ a \times b = b \times a \]
Example:
Multiply 54,678 × 785
Step 1: Vertical multiplication
\[ \begin{array}{r} 54\,678 \\ \times 785 \\ \hline 273\,390 \quad (\text{54,678 × 5, ones place}) \\ 4\,374\,240 \quad (\text{54,678 × 80, tens place}) \\ 38\,274\,600 \quad (\text{54,678 × 700, hundreds place}) \\ \hline 42\,922\,230 \quad (\text{Total product}) \end{array} \]Step 2: Expanded form method
\[ 54,678 \times 785 = (54,678 \times 700) + (54,678 \times 80) + (54,678 \times 5) \] \[ = 38,274,600 + 4,374,240 + 273,390 = 42,922,230 \]Final Answer: 42,922,230
Notes: - Each partial product corresponds to the place value of the multiplier digits. - Multiplication is commutative: 785 × 54,678 also gives the same product. - Breaking down large multiplications into smaller steps helps understanding and accuracy.
Watch the Video Explanation:
Multiplication Table Challenge
Choose two numbers from the dropdowns below, enter your product, then check your answer. You can also see the step-by-step working.