What is a Percentage?
A percentage is a way to express a number as a fraction of 100. The term "percent" comes from the Latin "per centum," which means "by the hundred."
For example, \( 45\% \) is equivalent to \( \frac{45}{100} \) or 0.45.
Converting Decimals to Percentages and Vice Versa
1. Decimals to Percentages
Multiply the decimal by 100 and add the percent symbol (%).
\( 0.75 \) as a percentage: \( 0.75 \times 100 = 75\% \)
2. Percentages to Decimals
Divide the percentage by 100.
\( 30\% \) as a decimal: \( \frac{30}{100} = 0.30 \)
Calculating Percentages
1. Finding the Percentage of a Number
Multiply the number by the percentage (as a decimal).
What is 20% of 50? \( 0.20 \times 50 = 10 \)
2. Finding What Percentage One Number is of Another
Divide the part by the whole and multiply by 100.
What percentage is 20 of 80? \( \left( \frac{20}{80} \right) \times 100 = 25\% \)
3. Finding the Whole Given the Percentage
Divide the part by the percentage (as a decimal).
If 20 is 25% of a number, what is the number? \( \frac{20}{0.25} = 80 \)
Example Problems
- A shirt costs $50, and it's on sale for 20% off. How much will the shirt cost after the discount?
- There are 500 students in a school. If 60% of them are girls, how many girls are there?
- A test has 80 questions. If a student gets 75% correct, how many questions did they answer correctly?
Percentage Quiz
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What is 20% of 150?
Answer
\( 0.20 \times 150 = 30 \) -
Convert 0.45 to a percentage.
Answer
\( 0.45 \times 100 = 45\% \) -
If 45 is 15% of a number, what is the number?
Answer
\( \frac{45}{0.15} = 300 \) -
Convert 120% to a decimal.
Answer
\( \frac{120}{100} = 1.20 \)
Percentage Quiz
-
What is 20% of 150?
Answer
\( 0.20 \times 150 = 30 \) -
Convert 0.45 to a percentage.
Answer
\( 0.45 \times 100 = 45\% \) -
If 50 is 10% of a number, what is the number?
Answer
\( \frac{50}{0.10} = 500 \) -
Convert 250% to a decimal.
Answer
\( \frac{250}{100} = 2.50 \) -
What is 75% of 80?
Answer
\( 0.75 \times 80 = 60 \) -
A product costs $120 and is on sale for 15% off. How much is the discount?
Answer
\( 0.15 \times 120 = 18 \) dollars. -
Convert 0.07 to a percentage.
Answer
\( 0.07 \times 100 = 7\% \) -
What percentage is 40 out of 200?
Answer
\( \left( \frac{40}{200} \right) \times 100 = 20\% \) -
Convert 350% to a decimal.
Answer
\( \frac{350}{100} = 3.50 \) -
If 30 is 5% of a number, what is the number?
Answer
\( \frac{30}{0.05} = 600 \) -
What is 60% of 45?
Answer
\( 0.60 \times 45 = 27 \) -
Convert 0.005 to a percentage.
Answer
\( 0.005 \times 100 = 0.5\% \) -
What percentage is 50 out of 250?
Answer
\( \left( \frac{50}{250} \right) \times 100 = 20\% \) -
Convert 0.85 to a percentage.
Answer
\( 0.85 \times 100 = 85\% \) -
If 90 is 30% of a number, what is the number?
Answer
\( \frac{90}{0.30} = 300 \) -
Convert 180% to a decimal.
Answer
\( \frac{180}{100} = 1.80 \) -
What is 25% of 200?
Answer
\( 0.25 \times 200 = 50 \) -
Convert 0.33 to a percentage.
Answer
\( 0.33 \times 100 = 33\% \) -
What percentage is 70 out of 140?
Answer
\( \left( \frac{70}{140} \right) \times 100 = 50\% \) -
Convert 0.09 to a percentage.
Answer
\( 0.09 \times 100 = 9\% \) -
If 15 is 3% of a number, what is the number?
Answer
\( \frac{15}{0.03} = 500 \) -
Convert 220% to a decimal.
Answer
\( \frac{220}{100} = 2.20 \) -
What is 40% of 90?
Answer
\( 0.40 \times 90 = 36 \) -
Convert 0.125 to a percentage.
Answer
\( 0.125 \times 100 = 12.5\% \) -
What percentage is 5 out of 50?
Answer
\( \left( \frac{5}{50} \right) \times 100 = 10\% \) -
Convert 0.78 to a percentage.
Answer
\( 0.78 \times 100 = 78\% \) -
If 24 is 8% of a number, what is the number?
Answer
\( \frac{24}{0.08} = 300 \) -
Convert 270% to a decimal.
Answer
\( \frac{270}{100} = 2.70 \) -
What is 55% of 110?
Answer
\( 0.55 \times 110 = 60.5 \) -
Convert 0.01 to a percentage.
Answer
\( 0.01 \times 100 = 1\% \) -
What percentage is 10 out of 20?
Answer
\( \left( \frac{10}{20} \right) \times 100 = 50\% \)
Percentage Shortcuts for SAT Exam
-
50% is Half:
- To find 50% of a number, simply divide it by 2.
- Example: \( 50\% \) of 80 is \( \frac{80}{2} = 40 \).
-
10% is One Tenth:
- To find 10% of a number, move the decimal point one place to the left.
- Example: 10% of 250 is 25.0 (or simply 25).
-
1% is One Hundredth:
- To find 1% of a number, move the decimal point two places to the left.
- Example: 1% of 5000 is 50.
-
Use 10% to Find Other Percentages:
- Once you know 10% of a number, you can easily find 20% (by doubling the 10%), 30% (by tripling the 10%), and so on.
- Example: For 80, 10% is 8, so 20% is 16, 30% is 24, and so forth.
-
5% is Half of 10%:
- Once you've calculated 10% of a number, halve it to get 5%.
- Example: 5% of 80 is \( \frac{8}{2} = 4 \).
-
Combining Percentages:
- If you need to find 15% of a number, it's often easier to find 10% and 5% separately and then add them together.
- Example: 15% of 80 is 8 (10%) + 4 (5%) = 12.
-
Double and Halve Method for Multiplication:
- If you're multiplying two numbers and one is even, you can halve one number and double the other to make the multiplication easier.
- Example: \( 25 \times 16 \) is the same as \( 50 \times 8 \) or \( 100 \times 4 \), all equal to 400.
-
Percent to Decimal Conversion:
- To convert a percentage to a decimal, divide by 100 (or move the decimal point two places to the left).
- Example: \( 45\% \) as a decimal is 0.45.
-
Decimal to Percent Conversion:
- To convert a decimal to a percentage, multiply by 100 (or move the decimal point two places to the right).
- Example: 0.78 as a percentage is 78%.
-
Practice Mental Math:
- Regularly practicing mental math can greatly speed up your calculations. Over time, you'll start recognizing common percentages and their decimal equivalents.
Remember, while shortcuts can be helpful, it's also important to ensure you understand the underlying concepts. With practice, you'll find that many of these shortcuts become second nature!
