Edexcel GCSE Maths: Fractions, Decimals, and Percentages

Edexcel GCSE Maths: Fractions, Decimals, and Percentages

This tutorial covers the essential concepts of fractions, decimals, and percentages, exploring their conversions, basic operations, and practical applications in real-life scenarios.

1. Understanding the Basics

• Fractions: Represent parts of a whole. They consist of a numerator (top number) and a denominator (bottom number). For example, 3/4 represents three out of four equal parts.
• Decimals: Represent numbers less than one, using a decimal point to separate the whole number from the fractional part. For example, 0.75 represents three quarters of a whole.
• Percentages: Represent parts of a whole expressed as a fraction of 100. The symbol "%" denotes a percentage. For example, 75% represents three quarters of a whole.

2. Conversions

• Fraction to Decimal: Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75
• Decimal to Fraction: Write the decimal as a fraction with the denominator as a power of 10. Simplify the fraction if possible. For example, 0.75 = 75/100 = 3/4
• Percentage to Decimal: Divide the percentage by 100. For example, 75% = 75/100 = 0.75
• Decimal to Percentage: Multiply the decimal by 100. For example, 0.75 x 100 = 75%

3. Operations

Addition and Subtraction:

• Fractions: Find a common denominator before adding or subtracting numerators.
• Decimals: Align the decimal points and perform the operation as usual.
• Percentages: Convert to decimals before adding or subtracting.

Multiplication and Division:

• Fractions: Multiply numerators and denominators. Simplify the resulting fraction.
• Decimals: Multiply as usual, counting decimal places in the answer.
• Percentages: Convert to decimals before multiplying or dividing.

4. Applications in Financial Math

• Discounts: Calculate the discount amount by multiplying the original price by the discount percentage. Subtract the discount from the original price to find the sale price.
• Interest: Calculate the interest earned or paid by multiplying the principal amount by the interest rate and the time period.
• Profit and Loss: Calculate the profit or loss by subtracting the cost price from the selling price.

5. Real-Life Scenarios

• Discounts: Calculate discounts on clothing, electronics, and other products.
• Interest: Calculate interest earned on savings accounts or paid on loans.
• Statistics: Calculate percentages in surveys, data analysis, and probability.
• Recipes: Adjust recipe quantities using fractions and percentages.

6. Example Problems

1. Convert 2/5 to a decimal and a percentage.

• Decimal: 2/5 = 2 ÷ 5 = 0.4
• Percentage: 0.4 x 100 = 40%

2. Calculate the sale price of a $100 item with a 20% discount.

• Discount amount: $100 x 0.20 = $20
• Sale price: $100 - $20 = $80

3. Calculate the simple interest earned on $500 at a 5% interest rate for 2 years.

• Interest earned: $500 x 0.05 x 2 = $50

4. A survey found that 60% of students prefer pizza for lunch. If there are 200 students in the school, how many prefer pizza?

• Students who prefer pizza: 200 x 0.60 = 120

7. Practice Exercises

1. Convert the following fractions to decimals and percentages:
   • 1/2
   • 3/4
   • 2/3
2. Calculate the following:
   • 3/4 + 1/2
   • 0.75 - 0.25
   • 50% of 200
3. A store offers a 15% discount on all items. If a shirt costs $30, what is the sale price?
4. You borrow $1000 at a 10% interest rate for one year. How much interest will you pay?

8. Conclusion

Mastering fractions, decimals, and percentages is fundamental for success in GCSE Maths and everyday life. By understanding their conversions, operations, and applications, you can confidently tackle various mathematical problems and real-world scenarios. Remember to practice regularly to solidify your understanding.