Problem 21 - Elementary Algebra

Question

What percent is \(1.75\) of 50 ?

Step-by-Step Solution

Answer

1.75 is 3.5% of 50.

Step 1: Set Up the Equation

To find what percent 1.75 is of 50, set up the equation \( x = \frac{1.75}{50} \)

Step 2: Perform the Division

Divide 1.75 by 50: \[ x = \frac{1.75}{50} = 0.035 \]

Step 3: Convert to Percent

Convert the decimal 0.035 to a percentage by multiplying by 100: \[ x = 0.035 \times 100 = 3.5\% \]

Key Concepts

percentage

A percentage is a way of expressing a number as a fraction of 100. It is often used to compare relative sizes or to express proportions. For example, if you get 45 out of 50 questions correct on a test, your score can be expressed as a percentage: \[ \text{Percentage} = \left( \frac{45}{50} \right) \times 100 = 90\% \] Percentages are especially useful in everyday contexts like discounts, interest rates, and statistics. They help us understand the size of one quantity in relation to another.

When the problem asks what percent 1.75 is of 50, it's asking how large 1.75 is compared to 50, expressed as a part of 100.

• First, you find the ratio of 1.75 to 50.
• Then, you convert this ratio into a percentage.

Understanding percentages is essential for many topics in mathematics and practical life scenarios.

division

Division is one of the basic operations of arithmetic. It is the process of splitting a number into equal parts. In the context of our problem, we need to divide 1.75 by 50. This helps us find out what part one number (1.75) is of another number (50).

To do this calculation: \[ x = \frac{1.75}{50} \] When you perform this division, you get: \[ x = 0.035 \] Division helps break down problems into smaller, more manageable parts.

• It is the inverse of multiplication.
• Knowing how to divide numbers is crucial for converting parts into wholes and vice versa.

In our example, division is the step that helps us move from comparing two numbers to finding their ratio.

conversion to percentage

Once you have your result from the division, the next step is to convert it into a percentage. Percentages allow you to express the result in a form that's easy to understand and compare.

To convert a decimal to a percentage, multiply the decimal by 100: \[ 0.035 \times 100 = 3.5\% \] This gives you the percentage value.

• Multiplying by 100 shifts the decimal point two places to the right.
• This step translates the ratio into a form that's commonly used and understood.

Converting to percentage completes the process, allowing you to say that 1.75 is 3.5% of 50. This step is what makes your answer interpretable and useful in a broader context.