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Chapter 7: Problem 358

In the following exercises, simplify. $$ 83 \cdot 0 $$

Short Answer

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Step by step solution

01

Identify the operation

The exercise requires simplifying the expression by multiplying 83 by 0.
02

Apply the zero multiplication property

Any number multiplied by 0 equals 0. Therefore, no complex calculation is needed here.
03

Simplified result

The result of multiplying 83 by 0 is 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Zero Multiplication Property
One of the easiest multiplication rules to remember is the zero multiplication property.
It states that any number multiplied by zero will always result in zero, regardless of the number itself.
So, whether you multiply 83 by 0 or 1,000,000 by 0, the answer is always 0.
This is important because it simplifies many problems, making calculations faster.
For example, in the exercise given, the task was to find the result of 83 multiplied by 0.
The use of the zero multiplication property tells us immediately that the answer is 0, without needing complex calculations.
Basic Arithmetic
Basic arithmetic involves the fundamental operations of addition, subtraction, multiplication, and division.
Multiplication itself can be seen as repeated addition.
For example, multiplying 3 by 4 is like adding 3 together four times (3 + 3 + 3 + 3).
Even though the zero multiplication property might seem separate from basic arithmetic, it's incredibly useful.
It鈥檚 an immediate way to greatly simplify many problems.
So, understanding these basic principles is crucial for tackling more complex mathematical challenges.
Practicing these operations and properties helps in improving your overall math skills and also builds a strong foundation for higher-level math.
Multiplication Rules
Learning the rules of multiplication can make math much easier and more intuitive.
Besides the zero multiplication property, some key rules include:
  • Any number multiplied by 1 remains the same (e.g., 7 x 1 = 7).
  • Multiplication is commutative, meaning the order of numbers doesn鈥檛 matter (e.g., 4 x 5 is the same as 5 x 4).
  • Multiplication is associative, so grouping numbers doesn鈥檛 change the result (e.g., (2 x 3) x 4 is the same as 2 x (3 x 4)).
  • Multiplication distributes over addition, which means a(b + c) is the same as ab + ac.
All these rules help make math problems easier to solve.
Mastering these can lead to more efficient and confident calculations.

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