Hello there. In this education & mathematics post, I would like to cover the keyword of. There are actually quite a few cases where the keyword **of** is used in the math setting. For the most part the keyword of means to take a portion of something. This post covers the different cases with this keyword.

## Topics

- Taking A Part/Fraction Of A Whole
- Multiplying Fractions Case
- Percentages
- Sample Of A Whole

## Taking A Part/Fraction Of A Whole

The keyword **of** means to take a part or fraction of a whole. As one example one half of 50 is 25. The number fifty is the whole, the number 25 is the part of a whole. The half represents the fraction of the whole.

**Example One**

Another example would be one quarter of 1000. Taking one quarter of 1000 means to divide 1000 by 4 to obtain 250. One thousand is the whole and the number 250 is the part of the whole.

**Example Two**

One half of what number is 250?

Let `x`

be the unknown number. Set up the equation as follows and then solve for `x`

.

What number divided by 2 gives 250. It is 500. Half of 500 gives 250.

## Multiplying Fractions Case

When it comes fractions and multiplying fractions in particular the keyword **of** means multiply. Here are a few examples.

**Example One**

What is one half of 200?

**Example Two**

What is four sevenths of 2100?

**Example Three**

You can take a fraction of a fraction. What is one third of seven tenths?

## Percentages

Percentages deal with parts of a whole. One percent is one of each 100 or 1/100 as a fraction. In the following examples the percentages are converted into fractions before multiplying fractions.

**Example One**

What is 10% of 300?

Ten percent is 10 out of 100 which can be reduced to 1 out of 10. This one tenth is multiplied with 300 to obtain 30.

**Example Two**

A country's tax rate on purchases is 8%. If Maria's purchases before tax comes to $230, how much tax does Maria pay?

Maria would pay $18.40 in taxes on top of the $230 purchase.

**Example Three**

Percentages can be above 100% sometimes. What is 550% of 20?

## Sample Of A Whole

The keyword **of** can be applied to introductory data management and introductory statistics.

A population is a group you want to get information from. It is often not practical to obtain information from every member from a population. It takes time and can cost a lot of money to do so. Taking a sample of the population involves taking a portion of the population to collect data with less time and less cost. A sample's size is less than the population.

When a sample is taken, the sample is part **of** the greater population. Information can be gathered from the sample to estimate characteristics or properties from the larger population.

Posted with STEMGeeks