Question

Solve the percent problem. \(12 \%\) of 5 is what number?

Short answer

12% of 5 is 0.6.

Step-by-step solution

Convert the Percent into a Decimal

To work with percents in numerical calculations, we first need to convert them into decimals. We do this by dividing the percent by 100. So, 12% becomes 0.12.

Set up the Multiplication Problem

We are asked to find what number is 12% of 5. 'Of' in math often means multiplication. Therefore, we set up the multiplication problem as such: \(0.12 * 5\).

Solve the Multiplication Problem

Now we simply multiply 0.12 by 5. This equals 0.6.

Key concepts

Converting Percents to Decimals

Understanding how to convert percents to decimals is crucial for solving percent problems efficiently. A percent represents a part per hundred, signaling how many pieces of a whole we have if that whole is divided into 100 equal parts. To convert a percentage to a decimal, simply divide it by 100.

This division by 100 can be easily performed by moving the decimal point two places to the left. For example, to convert 12% into a decimal, we move the decimal two places left, giving us 0.12. Remember that percent literally means 'per hundred', so you are essentially finding how many 'per hundred' units you have when you convert to a decimal. This step forms the foundation for performing further arithmetic operations involving percentages.

Percent of a Number

The phrase 'percent of a number' can be a tricky concept to grasp, but it's a common one found in mathematics and daily life. Whenever you encounter 'of' in the context of percentages, it typically signifies multiplication. Therefore, finding a certain percent 'of' a number involves turning the percent into a decimal and then multiplying that decimal by the number in question.

For instance, when asked to find 12% of 5, you first convert 12% to a decimal, which is 0.12, and then multiply this decimal by 5. This multiplication translates to finding 12 parts out of 100 of the number 5, which is a way to scale down the number proportionally to the given percent.

Multiplication in Percentages

Multiplying percentages is an extension of the previous concepts and is vital when determining a portion of a quantity. After the conversion of the percent to a decimal, multiplication allows you to apply that percent to find the actual numerical part it represents of some whole value.

It's important to understand that when you multiply a decimal (which is a percent converted into a decimal form) by a number, you're essentially partitioning that number into a number of pieces defined by the decimal. For instance, multiplying 0.12 by 5 means dividing 5 into 100 pieces and taking 12 of those pieces, which yields the answer of 0.6. This practice is not limited to simple calculations; it extends to more complex scenarios, like calculating discounts, interest rates, and proportional distributions in statistics.