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.
Step-by-Step Working