Exploring fractions, decimals, and percentages reveals their interconnectedness and utility in maths and real-life scenarios. This section aims to solidify your understanding, offering step-by-step calculations and examples to navigate through these concepts effectively.
Proper and Improper Fractions
Fractions express parts of a whole, defined by a numerator and a denominator.
![Fractions illustration](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F721506d7-b2c5-4967-97a9-2f64b024b5a9-file.png&w=1200&q=75)
- Proper Fractions: Where the numerator is smaller than the denominator, e.g., .
![Proper Fraction illustration](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F4913a4ce-eb99-4650-b68e-b067e2f43d90-file.png&w=1080&q=75)
Image courtesy of BYJUS
- Improper Fractions: Where the numerator exceeds or equals the denominator, e.g., .
![Improper Fraction illustration](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fdb46dd08-6d32-43e7-b7e1-cf7a94a82c05-file.png&w=1080&q=75)
Image courtesy of Twinkl
Improper fractions can transform into mixed numbers, blending whole numbers with fractions, like .
Example: Converting Improper Fractions to Mixed Numbers
Question: Convert into a mixed number.
Solution:
1. Divide 11 by 4: with a remainder of 3.
2. Express as a mixed number: .
Thus, converts to .
Decimals
Decimals offer another perspective for representing fractions, delineating the whole from the fractional part via a decimal point.
![Fractions to Decimals](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F92532760-23df-4246-a30f-c9886f5799aa-file.png&w=1200&q=75)
Image courtesy of Cuemath
Example: Converting Fractions to Decimals
Question: Convert to decimal.
Solution:
Percentages
Percentages frame fractions out of 100, simplifying comparisons and proportions.
![Decimal to Percent](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F28a2d52f-d23d-404d-9894-41ad2dd4ccf2-file.png&w=1080&q=75)
Example: Converting Decimals to Percentages
Question: Convert 0.2 to a percentage.
Solution:
Applying Concepts
Applying these conversions is crucial across financial calculations, measurements, and data analysis.
Real-life Application: Calculating Discounts
Scenario: A 20% discount on a £50 jacket. What's the final price?
Solution:
1. Convert 20% to decimal: .
2. Calculate discount: .
3. Deduct discount from original price: .
Final price: £40.