Problem 50 - Algebra for College Students

Question

15 is what percent of \(150 ?\)

Step-by-Step Solution

Answer

15 is 10% of 150.

Step 1: Develop the Percentage Formula

The formula to find what percent one number is of another is given by \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \]. Here, 15 is the part and 150 is the whole.

Step 2: Insert the Values

Substitute the values into the formula: \[ \text{Percentage} = \frac{15}{150} \times 100 \].

Step 3: Simplify the Fraction

Simplify the fraction \[ \frac{15}{150} = \frac{1}{10} \].

Step 4: Calculate the Percentage

Multiply the simplified fraction by 100: \[ \frac{1}{10} \times 100 = 10 \].

Step 5: Conclude the Answer

Thus, 15 is 10% of 150.

Key Concepts

percentage formula

To understand how to calculate percentages, it's essential to grasp the basic percentage formula.
The formula is useful for determining what percent one number (the part) is of another number (the whole).
It's given by: \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \].
The 'part' is the portion of the whole that you're interested in.
In our example, the 'part' is 15, and the 'whole' is 150.
By substituting these values into the formula, you can find the desired percentage.

part-whole relationship

The part-whole relationship is a fundamental concept when working with percentages.
Think of it as understanding how a portion (part) relates to the total amount (whole).
For instance, if you have 15 out of 150, this means 15 is the part and 150 is the whole.
This relationship allows you to see how big or small the part is compared to the whole.
Understanding this makes it easier to visualize and compute percentages using the formula mentioned earlier.

fractions simplification

Simplifying fractions is a crucial step in many percentage calculations.
When you simplify a fraction, you make the numbers smaller and easier to work with without changing its value.
For example, to simplify \[ \frac{15}{150} \], you divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).
In this case, both 15 and 150 can be divided by 15, giving: \[ \frac{15 \div 15}{150 \div 15} = \frac{1}{10}\].
This simplified fraction is then used to find the percentage in the next step by multiplying by 100, resulting in \[ \frac{1}{10} \times 100 = 10\text{\text{%}}.\].
Remember, simplifying fractions makes your calculations cleaner and more straightforward.