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Magazine Chapter 9: Problem 12
Rashid left a \(\$ 15\) tip for a \(\$ 75\) restaurant bill. What percent tip did he leave?
Short Answer
Expert verified
Rashid left a 20% tip.
Step by step solution
01
Understand the problem
We need to find out what percent a tip of \(15 is of a \)75 restaurant bill.
02
Write the formula for percent
The formula to find the percentage is \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \).
03
Assign values to the formula
In this case, the part is \(15 and the whole is \)75. So, the formula becomes \( \text{Percentage} = \frac{15}{75} \times 100 \).
04
Simplify the fraction
Simplify \( \frac{15}{75} \) to get \( \frac{1}{5} \).
05
Calculate the percentage
Multiply \( \frac{1}{5} \times 100 = 20\text{\text{\%}} \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
percentage formula
To calculate percentages, you can use a simple formula. The formula is: \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \). Here, 'Part' refers to the amount you are considering, and 'Whole' is the total amount. For example, if Rashid left a \(15 tip on a \)75 bill, we consider \(15 as the 'Part' and \)75 as the 'Whole'.
Using the formula, you place these values into it like this: \[ \text{Percentage} = \frac{15}{75} \times 100 \].
This formula helps convert the fraction into a percentage, making it easier to compare and understand.
Whenever you're stuck with a percentage problem, remember to use this simple formula!
Using the formula, you place these values into it like this: \[ \text{Percentage} = \frac{15}{75} \times 100 \].
This formula helps convert the fraction into a percentage, making it easier to compare and understand.
Whenever you're stuck with a percentage problem, remember to use this simple formula!
simplifying fractions
Simplifying fractions is an important step in solving many mathematical problems, including percentage calculations.
To simplify a fraction, divide the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). In Rashid's case, we have the fraction \( \frac{15}{75} \).
The GCD of 15 and 75 is 15.
Now, your fraction is much simpler and easier to work with, making the final calculation more straightforward.
To simplify a fraction, divide the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). In Rashid's case, we have the fraction \( \frac{15}{75} \).
The GCD of 15 and 75 is 15.
- Step 1: Divide the numerator and denominator by 15:
\( \frac{15 \text{ (numerator)}}{75 \text{ (denominator)}} = \frac{15 \textdiv 15}{75 \textdiv 15} = \frac{1}{5} \) - Step 2: After simplifying, the fraction becomes \( \frac{1}{5} \).
Now, your fraction is much simpler and easier to work with, making the final calculation more straightforward.
real-world math problems
Understanding how to apply mathematical concepts to real-world situations is valuable.
Consider Rashid's tip at a restaurant as an example. Being able to calculate the percentage of a tip is useful in everyday scenarios.
Let's break down this process:
Consider Rashid's tip at a restaurant as an example. Being able to calculate the percentage of a tip is useful in everyday scenarios.
Let's break down this process:
- Step 1: Identify the 'Part' (tip = \(15) and the 'Whole' (bill = \)75).
- Step 2: Use the percentage formula: \( \text{Percentage} = \frac{15}{75} \times 100 \).
- Step 3: Simplify the fraction: \( \frac{15}{75} = \frac{1}{5} \).
- Step 4: Convert to a percentage: \( \frac{1}{5} \times 100 = 20\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text))))}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}ooooooooo% \).
This method can be applied to countless other real-world math problems. Whether it's taxes, discounts, or data statistics, knowing how to calculate percentages and work with fractions is essential.
