krit.club logo

Number - Fractions, Decimals, and Percentages

Grade 10IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Conversion between fractions, decimals, and percentages (FDP).

•

Simplifying fractions and finding common denominators for addition and subtraction.

•

Converting recurring decimals into fractions using algebraic methods.

•

Calculating percentage increase and decrease using multipliers.

•

Understanding Reverse Percentages to find the original value before a change.

•

Distinguishing between Simple Interest (linear growth) and Compound Interest (exponential growth).

📐Formulae

Percentage Change=New Value−Original ValueOriginal Value×100\text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100

Multiplier for Increase=1+%100\text{Multiplier for Increase} = 1 + \frac{\%}{100}

Multiplier for Decrease=1−%100\text{Multiplier for Decrease} = 1 - \frac{\%}{100}

Original Value=New ValueMultiplier\text{Original Value} = \frac{\text{New Value}}{\text{Multiplier}}

Compound Interest Total Value (A)=P(1+r100)n\text{Compound Interest Total Value (A)} = P(1 + \frac{r}{100})^n

Simple Interest (I)=P×R×T100\text{Simple Interest (I)} = \frac{P \times R \times T}{100}

💡Examples

Problem 1:

Convert the recurring decimal 0.7˙0.\dot{7} to a fraction in its simplest form.

Solution:

79\frac{7}{9}

Explanation:

Let x=0.777...x = 0.777.... Then 10x=7.777...10x = 7.777.... Subtracting the first equation from the second gives 10x−x=7.777...−0.777...10x - x = 7.777... - 0.777..., which simplifies to 9x=79x = 7. Therefore, x=79x = \frac{7}{9}.

Problem 2:

A car's value depreciates by 15% each year. If the car is worth $12,000 now, what will it be worth in 3 years?

Solution:

$7,369.50

Explanation:

This is a compound depreciation problem. Use the formula A=P(1−r)nA = P(1 - r)^n. Here, P=12000P = 12000, r=0.15r = 0.15, and n=3n = 3. Calculation: 12000×(0.85)3=12000×0.614125=7369.512000 \times (0.85)^3 = 12000 \times 0.614125 = 7369.5.

Problem 3:

The price of a television after a 20% sales tax is added is $432. Find the original price before the tax.

Solution:

$360

Explanation:

This is a reverse percentage problem. The 432represents120432 represents 120% of the original price (1.20 as a multiplier). To find the original, divide the new price by the multiplier: 432 \div 1.2 = 360$.