Question

Identify the unknown amount as the percent, part, or whole. \(10 \%\) of 80 is what number?

Short answer

Answer: 10% of 80 is 8.

Step-by-step solution

Understand the problem

We're asked to find 10% of 80, which means we need to calculate the part that represents 10% of thetotal amount.

Write down the given values and percentage formula

Percentage formula: \(\frac{Part}{Whole} = Percent\) Given: Percent (P) = 10% Whole (W) = 80 Let the unknown part be "x".

Set up the equation with the given values

We will use the percentage formula and plug in the given values: \(\frac{x}{80} = 10 \%\)

Convert percentage to decimal

To solve for "x", first convert 10% to its decimal form: Decimal form of 10% = \(\frac{10}{100} = 0.1\) Now, the equation becomes: \(\frac{x}{80} = 0.1\)

Solve for the unknown part, x (the number)

To find the value of x, multiply both sides of the equation by the whole (80): \(x = 0.1 \times 80\) Multiply the values: \(x = 8\)

State the answer

The unknown part, representing 10% of 80, is 8.

Key concepts

Percent Formula

When tackling percentage problems, it's important to have a solid understanding of the percent formula, which is a pivotal tool. The formula is expressed as \( \frac{Part}{Whole} = Percent \) in its simplest form. This equation helps you to find one of the three components when the other two are known. For example, if you know the whole (the total amount) and the percent (the portion expressed as a percentage), you can solve for the part. This is exactly what we did in our exercise, where we were given the whole (80) and the percent (10%) and asked to find the part.

Decimal Conversion

Understanding how to convert percentages to decimals is crucial in solving percentage problems efficiently. To transform a percentage into a decimal, simply divide by 100. This step is necessary because percentages are based on the value out of 100, but when doing calculations, we require a number in its decimal form for multiplication or division. For instance, 10% becomes 0.1 when converted to a decimal (\(\frac{10}{100} = 0.1\)). Remember that moving the decimal point two places to the left also achieves the same conversion. This method was utilized in our exercise to convert 10% to 0.1 before we could proceed with solving for the unknown part.

Part Whole Percent

The 'part whole percent' relationship is a fundamental aspect of percentage problems encompassing the understanding of how these three elements interact with each other. 'Part' refers to a portion of the 'whole', which is the total quantity or amount. 'Percent' indicates the ratio or fraction of the part relative to the whole, expressed in hundredths. Learning to identify which of these elements is the unknown variable in a question is key, as it directs the approach for finding the solution. In our exercise, 'part' was the unknown, 'whole' was given as 80, and 'percent' was specified as 10%. These components were applied to the percent formula to deduce the unknown 'part', which was the objective of the exercise.