Here's a guide to learn how to calculate percentages, complete with practice questions and solutions:
Introduction:
Calculating percentages is an essential skill in maths. It helps us understand parts of a whole and compare quantities. Let's dive into the world of percentages and become percentage masters!
1. Understanding Percentages:
- Percentage is a way to express a part of a whole as a fraction of 100.
- It is denoted by the symbol "%."
- For example, if you have 30 out of 100 marbles, you can say you have 30%.
- If you have recaptured 900 out of 1000 escaped crafty racoons, you can chop off the extra zeroes - 90 of 100 - and say you have 90% of those escaped crafty racoons, who can now be safely sent back to their natural habitat with their tiny suitcases containing all of the stuff they nabbed.
2. Converting Percentages to Decimals and Fractions:
- To convert a percentage to a decimal, divide it by 100.
Example: 50% = 50 ÷ 100 = 0.5
- To convert a percentage to a fraction, write it over 100 and simplify.
Example: 25% = 25/100 = 1/4
- We get to 1/4 by finding the Greatest Common Factor (GCF). That's just the biggest number we can use to divide both numbers. 25 goes into 25 ONCE and goes into 100 FOUR times, which gives us 1/4.
3. Calculating Percentages:
- To find a percentage of a quantity, multiply the quantity by the percentage and then multiply that by the fractional version of the percentage.
Example: What is 20% of 80? 80 × 20% = 80 × 0.2 = 16
Practice Questions:
1. Calculate 15% of 200 of angry turkeys.
2. Find 40% of 150 rapid old people.
3. What is 75% of 80 clones?
Solutions
1. 15% of 200 = 200 × 15% = 200 × 0.15 = 30 angry turkeys
2. 40% of 150 = 150 × 40% = 150 × 0.4 = 60 rapid old people
3. 75% of 80 = 80 × 75% = 80 × 0.75 = 60 clones
4. Finding the Whole:
- To find the whole when given a part and the percentage, divide the part by the percentage and multiply by 100.
Example: 25 is 20% of what number? 25 ÷ 20% = 25 ÷ 0.2 = 125
Practice Questions:
1. 12 is 60% of what number?
2. 30 is 25% of what number?
3. 45 is 15% of what number?
Solutions
1. 12 ÷ 60% = 12 ÷ 0.6 = 20
2. 30 ÷ 25% = 30 ÷ 0.25 = 120
. 45 ÷ 15% = 45 ÷ 0.15 = 300
5. Calculating Percentage Change:
- To find the percentage increase or decrease between two values, use the following formula:
Percentage Change = ((New Value - Old Value) ÷ Old Value) × 100
- A positive percentage indicates an increase, while a negative percentage indicates a decrease.
Practice Questions:
1. The price of a mini toenail clipping robot servant increased from $10 to $15. What is the percentage increase?
2. Sarah's magical fart test score decreased from 80 to 70. What is the percentage decrease?
Solutions
1. Percentage Increase = ((15 - 10) ÷ 10) × 100 = (5 ÷ 10) × 100 = 50%. The price of a mini toenail clipping robot servant increased by 50%
2. Percentage Decrease = ((70 - 80) ÷ 80) × 100 = (-10 ÷ 80) × 100 = -12.5%. Sarah's magical fart test score decreased by 12.5%
Remember to practice regularly to become a percentage whiz! With time and practice, calculating percentages will become second nature to you. Keep up the great work!