Problem 76
Question
$$ \text { Find } 24 \% \text { of } 75 \text {. } $$
Step-by-Step Solution
Verified Answer
24% of 75 is 18.
1Step 1: Understand Percentage
A percentage represents a fraction out of 100. So, 24% means 24 out of 100 or 0.24 in decimal form.
2Step 2: Convert Percentage to Decimal
Convert 24% to a decimal by dividing 24 by 100: \[\frac{24}{100} = 0.24\]
3Step 3: Multiply by the Given Number
To find 24% of 75, multiply the decimal form of the percentage by the number: \[0.24 \times 75 = 18\]
4Step 4: Interpret the Result
The result of the multiplication gives the value of 24% of 75, which is 18.
Key Concepts
converting percentagesdecimal multiplicationproblem-solving steps
converting percentages
Converting percentages into decimals is an essential skill in mathematics. It helps simplify calculations and makes it easier to perform operations like multiplication and division. To convert a percentage to a decimal, you divide the percentage by 100. This is because 'percent' means 'per hundred'.
For example, converting 24% to a decimal involves dividing 24 by 100:
\(\frac{24}{100} = 0.24\)
This means that 24% is equivalent to 0.24 in decimal form. This might seem like a small step, but it is crucial for performing further calculations accurately. Remember, anytime you have a percentage, just divide by 100 to get the decimal form.
For example, converting 24% to a decimal involves dividing 24 by 100:
\(\frac{24}{100} = 0.24\)
This means that 24% is equivalent to 0.24 in decimal form. This might seem like a small step, but it is crucial for performing further calculations accurately. Remember, anytime you have a percentage, just divide by 100 to get the decimal form.
decimal multiplication
Once you have converted the percentage to a decimal, the next step is to multiply it by the given number. Decimal multiplication is similar to regular multiplication, with the main difference being the placement of the decimal point in the final product.
Here’s an example to illustrate:
To find 24% of 75, you first convert 24% to a decimal (which we've already done as 0.24). You then multiply the decimal by 75:
\[ 0.24 \times 75 \]
When performing this multiplication, you get:
\[ 0.24 \times 75 = 18 \]
The key is to align the decimal points correctly after performing the multiplication. Practice makes perfect, so keep trying more problems to become comfortable with this process.
Here’s an example to illustrate:
To find 24% of 75, you first convert 24% to a decimal (which we've already done as 0.24). You then multiply the decimal by 75:
\[ 0.24 \times 75 \]
When performing this multiplication, you get:
\[ 0.24 \times 75 = 18 \]
The key is to align the decimal points correctly after performing the multiplication. Practice makes perfect, so keep trying more problems to become comfortable with this process.
problem-solving steps
Solving percentage problems involves a systematic approach. Here are clear steps to follow to ensure you get the correct answer:
1. **Understand the Percentage**: Recognize that a percentage is a way of expressing a number as a part of 100.
2. **Convert the Percentage to a Decimal**: Divide the percentage by 100 to convert it to a decimal form.
3. **Multiply by the Given Number**: Use the decimal form of the percentage and multiply it by the number provided in the problem.
Following these steps ensures a structured approach to solving percentage problems. Let’s break down these steps with our example:
1. We need to find 24% of 75.
2. Convert 24% to a decimal: \( 24\frac{24}{100} = 0.24\)
3. Multiply: \[ 0.24 \times 75 = 18 \]
By consistently following these steps, you can solve percentage problems accurately and efficiently.
1. **Understand the Percentage**: Recognize that a percentage is a way of expressing a number as a part of 100.
2. **Convert the Percentage to a Decimal**: Divide the percentage by 100 to convert it to a decimal form.
3. **Multiply by the Given Number**: Use the decimal form of the percentage and multiply it by the number provided in the problem.
Following these steps ensures a structured approach to solving percentage problems. Let’s break down these steps with our example:
1. We need to find 24% of 75.
2. Convert 24% to a decimal: \( 24\frac{24}{100} = 0.24\)
3. Multiply: \[ 0.24 \times 75 = 18 \]
By consistently following these steps, you can solve percentage problems accurately and efficiently.
Other exercises in this chapter
Problem 75
For exercises 15-100, evaluate. $$ (4-9)^{2}-3(-1) $$
View solution Problem 75
For exercises 1-80, evaluate. $$ \left(\frac{6+5 \cdot 0}{6}\right)^{2} $$
View solution Problem 76
For exercises \(75-80\), rewrite the fraction as an equivalent fraction with the given denominator. $$ \frac{2}{7} ; 56 $$
View solution Problem 76
For exercises 1-80, evaluate. $$ \left(\frac{9+2 \cdot 0}{9}\right)^{2} $$
View solution