Problem 55 - College Algebra and Calculus: An Applied Approach

Question

Use a calculator to solve.\(35 \%\) of 68

Step-by-Step Solution

Answer

The result of \(35\%\) of 68 can be found by multiplying \(0.35\) and \(68\). Use a calculator to perform the calculation if necessary.

Step 1: Express Percentage as a Decimal

To calculate a percentage of a number, we first express the percentage in decimal form. Percentage means 'out of 100', so \(35\%\) can be written as \(0.35\). This is achieved by dividing the percentage by 100.

Step 2: Multiply the Given Number

Next, we multiply the given number (68 in this case) by the decimal we obtained in step 1: \(0.35 \times 68 \)

Step 3: Perform the Calculation

Finally, perform the multiplication operation to obtain the result. Use a calculator if necessary for this step.

Key Concepts

Decimal Conversion

Understanding how to convert a percentage into a decimal is a key part of solving many math problems. Percentages are simply another way of expressing fractions; they mean "out of 100". For instance, to convert \(35\%\) to a decimal, you divide by 100, resulting in \(0.35\).
This process is fundamental because it enables us to perform operations like multiplication more easily. By changing from percentage to decimal, we streamline calculations, such as finding a percentage of a number, into simpler numeric operations.

Multiplication

Once the percentage is converted to a decimal, our task becomes straightforward: multiply this decimal by the desired number. In our exercise, after converting \(35\%\) to \(0.35\), we multiply it by 68. This involves multiplying the decimal form of the percentage with the target number to find what \(35\%\) of 68 is. Multiplication in this context means repeated addition of the number by the decimal part, effectively scaling the whole value down to the specified percentage, which is often more intuitive than directly interpreting percentages.

Calculator Use

Using a calculator can be a great way to check your work or speed up calculations, especially with decimals and larger numbers. Calculators are designed to handle these tasks effortlessly. For example, multiplying \(0.35\) by 68 can be done in seconds with a calculator.
To perform this operation, ensure your calculator is set to use decimal numbers. Simply input the numbers into the calculator: type \(0.35\), then press the multiplication button (usually \("\times"\)), enter \(68\), and finally hit the equals button (\(="\)) to see the result, which will prompt the calculator to display 23.8.
Using a calculator not only helps confirm the arithmetic but also builds confidence in your calculations.

Mathematics Problem Solving

Mathematics problem solving often involves a series of strategic steps, much like a roadmap guiding you from question to solution. Understanding this structure is crucial. When tasked with a problem like finding \(35\%\) of 68, start by breaking it down into manageable steps as shown.
You first convert the percentage to a decimal, use multiplication to find the fraction of the number, and if needed, confirm with a calculator. This stepwise approach ensures clarity and reduces errors.
Developing problem-solving skills in mathematics involves understanding the concepts behind these steps, which can then be applied to a wide range of problems, building your competence and confidence in handling numbers effectively.