Question

Translate to an equation and solve. What number is \(15 \%\) of \(78 ?\)

Short answer

Answer: 11.7

Step-by-step solution

Convert the percentage to a decimal

To convert the percentage to a decimal, we simply divide it by 100. So, 15% = \(\frac{15}{100}\) = 0.15.

Multiply the decimal by the number

Now that we have found the decimal equivalent of the percentage, we need to multiply it by the number to find the answer. In this case, we will multiply 0.15 by 78: 0.15 * 78 = 11.7

Write the final answer

15% of 78 is 11.7, so the number we are looking for is 11.7.

Key concepts

Converting Percentages to Decimals

Understanding how to change percentages into decimals is an essential skill for many math problems, including those that deal with money, statistics, and various real-world scenarios. The process is simple: to convert a percentage to a decimal, we divide the percentage by 100. This is because the word 'percent' means 'per hundred'. For example, converting 15% to a decimal is as straightforward as dividing 15 by 100, which gives us 0.15. It's important to recognize that moving the decimal two places to the left accomplishes the same result.

This step is crucial as it prepares us to perform various operations with the percentage value in decimal form, such as multiplying it with other numbers to find a portion of a quantity, which is exactly what we do when we compute discounts, interest rates, and other percentage-based calculations.

Multiplying Decimals

Multiplying decimals is a fundamental operation that can initially seem tricky but follows a simple logic. When we multiply a decimal by a whole number, we apply the same principles as we would with whole numbers. Begin by multiplying without considering the decimal place. After the multiplication, the key step is to place the decimal point in the correct place. The position of the decimal in the product is determined by the sum of the number of decimal places in the numbers being multiplied.

For instance, when we multiply 0.15 (two decimal places) by 78 (no decimal places), we start by multiplying as if there were no decimals: 15 * 78. We obtain a product and then reintroduce the decimal into the result, shifting it two places to the left to account for the two decimal places we initially ignored. This gives us the precise answer of 11.7. It's important to practice this process to foster accuracy when dealing with money, measurements, and other related applications.

Solving Basic Algebra Problems

When faced with a basic algebra problem, our aim is to find the unknown variable. In the context of the given exercise, the unknown variable can be represented by the letter 'x'. We start by setting up an equation. Here, 'x' is the number we seek, and it is described as being '15% of 78'. We express this as:
\[ x = 0.15 \times 78 \]
Algebra problems often involve one or more of these steps: setting up equations, manipulating expressions, and solving for the unknown. In this simple case, after converting the percentage to a decimal, we're directly multiplying to find 'x'.

Understanding how to isolate and solve for a variable is a foundational skill in algebra. These kinds of problems serve as building blocks for more complex equations and mathematical concepts. By mastering this step-by-step approach, we build the competency to tackle a wide range of algebraic challenges.