# How to find the unknown factor

Multiplication and division, just as addition and subtraction, are the basic arithmetic operations. Not having learned to solve the examples on multiplication and division, the man will face many challenges, not only in the study of more complex areas of mathematics, but even in the most ordinary affairs of life. Multiplication and division are closely linked, and unknown components of examples and problems at one of these actions are calculated by another action. It should be clearly understood that in dealing with the examples do not care what kind of items you divide or multiply.

### You will need:

- multiplication table; - A calculator or paper and pencil.

## Instruction how to find the unknown factor

Step 1:

Record the desired example. Designate an unknown factor like x. An example might look like this: a * x = b. Instead, the factor a and b in the example works can be any letter or number. Remember the basic multiplication properties: from the relocation of the factors does not change the product. So it's an unknown factor could be absolutely anywhere.

Step 2:

In order to find the unknown factor in an example where only two factors, you just need to divide the work of a known factor. That is, it is done as follows: x = b / a. If you find it difficult to operate with abstract values, try to imagine this problem in the form of concrete objects. You know how you just apples and how many people they will have, but do not know for how many apples will get everyone. For example, you have 5 family members and apples turned 15. The number of apples, each designed, as a mark x. Then the equation will look like this: 5 (apples) * x = 15 (apples). Unknown factor is in the same manner as in the equation with letters, that is, 15 apples divide by five members of the family, in the end it turns out that each of them ate 3 apples.

Step 3:

In the same way there is an unknown factor with a larger number of factors. For example, an example looks like a * b * c * x * = d. The idea is to find the factor, and so can be the same as in a fasting example: x = d / a * b * c. But you can reduce the equation to the more simple form, denoting the product of the factors known to any other letter - for example, m. Find, which is equal to m, multiplying the number of a, b and a: m = a * b * c. Then the entire sample can be represented as m * x = d, and the unknown quantity is equal to x = d / m.

Step 4:

If a known factor and the product is a fraction, Example solved in the same way as with integers. But in this case it is necessary to remember the rules of action with fractions. When multiplying fractions, the numerators and denominators of multiplied. When dividing fractions, the numerator of the dividend multiplied by the denominator of the divider, and the denominator of the dividend - in the numerator of the divider. That is, in this case, the example would look like this: a / b * x = c / d. To find the unknown value, it is necessary to divide the product of a known multiplier. That is, x = a / b: c / d = a * d / b * c.