# Basic Arithmetic Explanation

In general, basic arithmetic exercises consist of an equation with an unknown (the question mark). You will have to figure out what number should replace the question mark. For example:

3 + 7 *? = 24

1. 4
2. 3
3. 2
4. 1
5. 7
6. 5

You can enter all possible answers and you will see that the correct answer is 3.

3 + 7 * 3 = 3 + 21 = 24. However, this strategy will take too long, especially with more difficult exercises with many multiple choice options. It is better to always apply the method below to solve equations.

Order of calculation (exponentiation, square root, multiplication, division, addition, subtraction)

1. Eliminate parentheses, this should be done before all other operations.
2. Exponentiation and square roots, working from left to right.
3. Divide and multiply, from left to right.
4. Addition and subtraction, from left to right.

Solving an equation

The goal is to end with a question mark on one side of the is-sign (=) and the answer on the other side. As long as you perform the same transformation on both sides of the equation, the equation will be true.

This is based on the following principle:

2 = 2

If the same operation is performed on both sides, the equation will always be correct.

2 * 100 = 2 * 100

200 = 200

2 + 100 = 2 + 100

102 = 102

This seems a bit childish, but the principle is clear. This is useful when solving the next equation.

? * 100 - 100 = 200 * 3

We want to find the number which should replace the question mark, so we divide by 100 on both sides.

? * 100/100 - 100/100 = 200 * 3 / 100

This can be shortened:

? * 1 - 1 = 6

Now we add 1 on both sides.

? * 1 - 1 + 1 = 6 + 1

You can check whether the answer is correct by entering it at the place of the question mark in the exercise.

7 * 100 - 100 = 200 * 3

700 - 100 = 600

600 = 600

Examples

Example 1

6 / (5 + 1) *? - 10 = 12 * 6 - 6

Step 1: eliminate parentheses.

6 /6 * ? - 10 = 12 * 6 - 6

Step 2: division and multiplication, left to right

1 * ? - 10 = 72 - 6

? - 10 = 64

Step 3: You want to work towards the situation with a question mark on the left and the answer on the right. To do this, add 10 on both sides of the equation.

? - 10 + 10 = 64 + 10

Example 2

3 * ? + 3 - 9 = 12

Step 1: There are no parentheses or powers, so division and multiplication is the first step, from left to right. We want to work towards the situation with a question mark on the left and the answer on the right, so we divide everything by 3.

3 *? / 3 + 3 / 3-9 / 3 = 12/3?

? + 1 - 3 = 4

Step 2: Simplify (you could have done this as the first step.):

? + 1 - 3 = 4

? - 2 = 4

Step 3: You want to only keep a question mark on the left. To do this, add 2 on both sides of the is sign (=).

? - 2 + 2 = 4 + 2