# Just a simple arithmetic problem

• BobG
In summary, the purpose of a simple arithmetic problem is to practice and improve basic math skills, and it can be solved by following the order of operations. Using a calculator is allowed, but it is recommended to try solving mentally first. Common mistakes include not following the correct order, misreading the problem, and making calculation errors. To improve speed and accuracy, one can practice regularly, solve mentally, and double-check calculations.
BobG
Homework Helper
Easy arithmetic problem:

$$x=222,222,222,222,222,222,222^2-222,222,222,222,222,222,221^2$$

Find x.

$$x=(n+1)^2-n^2=2n+1$$
where $n=222,222,222,222,222,222,221$.
Therefore
$$x=444,444,444,444,444,444,443$$

I set N = 222,222,222,222,222,222 so that question becomes

(n+222)^2 - (n+221)^2

after which solving for n is straightforward

Not as nice as the first response, however

kevinferreira said:
$$x=(n+1)^2-n^2=2n+1$$
where $n=222,222,222,222,222,222,221$.
Therefore
$$x=444,444,444,444,444,444,443$$

mmm...

$$x=a^2-b^2=(a+b)(a-b)$$
but $$a-b = 1$$ so
$$x = a+b = 444,444,444,444,444,444,443$$

Last edited:

The solution to this problem is not as simple as it may seem. While the arithmetic involved is straightforward, the large numbers make it challenging to solve mentally. However, with the use of a calculator or by breaking the numbers down into smaller parts, we can find the value of x. The result is 444,444,444,444,444,444,443. This type of problem highlights the importance of breaking down complex tasks into smaller, more manageable pieces in order to find a solution. It also showcases the power and convenience of using tools such as calculators in scientific and mathematical calculations.

## 1. What is the purpose of a simple arithmetic problem?

The purpose of a simple arithmetic problem is to practice and improve one's basic math skills, such as addition, subtraction, multiplication, and division.

## 2. How can I solve a simple arithmetic problem?

To solve a simple arithmetic problem, you can follow the basic order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

## 3. Can I use a calculator to solve a simple arithmetic problem?

Yes, you can use a calculator to solve a simple arithmetic problem. However, it is recommended to first try solving it mentally to improve your math skills.

## 4. What are some common mistakes people make when solving a simple arithmetic problem?

Some common mistakes people make when solving a simple arithmetic problem include not following the correct order of operations, misreading or misinterpreting the problem, and making simple calculation errors.

## 5. How can I improve my speed and accuracy in solving simple arithmetic problems?

To improve your speed and accuracy in solving simple arithmetic problems, you can practice regularly, try to solve problems mentally without using a calculator, and double-check your calculations for any errors.

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