Title: Percentages and Math

Instructions: 1. Read the following information carefully. 2. Complete the worksheet by solving the given problems. 3. Show all your work and write your answers in the spaces provided. 4. Ask your teacher for assistance if needed.

Subtopic 1: How to Use Percentages

A percentage is a way to express a part of a whole as a fraction of 100. It is denoted by the symbol “%”. To calculate a percentage, divide the part by the whole and multiply by 100.

Example: What is 25% of 80? Step 1: Divide 25 by 100: 25 ÷ 100 = 0.25 Step 2: Multiply 0.25 by 80: 0.25 × 80 = 20 Answer: 25% of 80 is 20.

Worksheet: 1. Calculate the following percentages: a) 15% of 200 = ___ b) 40% of 250 = ___ c) 75% of 120 = ___

Subtopic 2: Conversion between Fractions and Percentages

To convert a fraction to a percentage, multiply it by 100. To convert a percentage to a fraction, divide it by 100 and simplify if necessary.

Example: Convert 3/5 to a percentage. Step 1: Multiply 3/5 by 100: (3/5) × 100 = 60% Answer: 3/5 is equivalent to 60%.

Worksheet: 2. Convert the following fractions to percentages: a) 2/3 = __% b) 5/8 = __% c) 3/10 = ___%

1. Convert the following percentages to fractions: a) 75% = ___ b) 20% = ___ c) 40% = ___

Subtopic 3: Percentage Change over Time

To calculate a percentage change, subtract the original value from the new value, divide the result by the original value, and multiply by 100.

Example: A car’s price increased from $10,000 to $12,000. Calculate the percentage increase. Step 1: Subtract the original value from the new value: $12,000 - $10,000 = $2,000 Step 2: Divide $2,000 by $10,000: $2,000 ÷ $10,000 = 0.2 Step 3: Multiply 0.2 by 100: 0.2 × 100 = 20% Answer: The car’s price increased by 20%.

Worksheet: 4. Calculate the percentage change in the following situations: a) A population increased from 500 to 600. b) The price of a product decreased from $80 to $60. c) The temperature rose from 25°C to 30°C.

Subtopic 4: Real-World Applications

Percentages are used in various real-life situations, such as sales, chemistry, and the economy. They help us understand changes, discounts, concentrations, and more.

Example: A store is having a sale with a 30% discount on all items. If a shirt originally costs $40, what is the sale price? Step 1: Calculate the discount: 30% of $40 = 0.3 × $40 = $12 Step 2: Subtract the discount from the original price: $40 - $12 = $28 Answer: The sale price of the shirt is $28.

Worksheet: 5. Solve the following real-life problems: a) A chemistry solution is 15% concentrated. If you have 200 mL of the solution, how many milliliters are the solute? b) A store is offering a 20% discount on a $250 camera. What is the sale price? c) The GDP of a country increased by 5% from $1,000 billion. What is the new GDP?

Remember to show all your work and write your answers in the spaces provided. Good luck!