Fractions

Lesson Objectives

Define and identify different types of fractions.
Simplify and compare fractions.
Convert between improper fractions and mixed numbers.
Add, subtract, multiply, and divide fractions.

Lesson Introduction

Fractions are an essential part of mathematics that represent a part of a whole. Understanding how to work with fractions is vital in both everyday life and advanced math topics.

Lesson Content

Types of Fractions

Fractions can be categorized into:

Proper Fractions: The numerator is less than the denominator (e.g., \(\frac{3}{4}\)).
Improper Fractions: The numerator is greater than or equal to the denominator (e.g., \(\frac{7}{4}\)).
Mixed Numbers: A whole number combined with a proper fraction (e.g., \(1\frac{3}{4}\)).

Converting Between Improper Fractions and Mixed Numbers

Convert \(\frac{9}{4}\) to a mixed number:

Divide 9 by 4 → 9 ÷ 4 = 2 remainder 1

Answer: \(2\frac{1}{4}\)

Convert \(\frac{11}{3}\) to a mixed number:

11 ÷ 3 = 3 remainder 2

Answer: \(3\frac{2}{3}\)

Convert \(4\frac{2}{5}\) to an improper fraction:

\((4 \times 5 + 2 = 22)\)

Answer: \(\frac{22}{5}\)

Convert \(2\frac{3}{8}\) to an improper fraction:

\((2 \times 8 + 3 = 19)\)

Answer: \(\frac{19}{8}\)

Examples

Simplify \(\frac{18}{24}\):

GCD of 18 and 24 is 6 → \(\frac{18 \div 6}{24 \div 6} = \frac{3}{4}\)

Answer: \(\frac{3}{4}\)

Compare \(\frac{2}{5}\) and \(\frac{3}{4}\):

Find LCM of 5 and 4 = 20

\(\frac{2}{5} = \frac{8}{20}, \quad \frac{3}{4} = \frac{15}{20}\)

Answer: \(\frac{3}{4} > \frac{2}{5}\)

Add \(\frac{3}{8} + \frac{5}{8}\):

Same denominator → \(\frac{8}{8} = 1\)

Answer: 1

Subtract \(\frac{7}{10} - \frac{2}{10}\):

\(\frac{5}{10} = \frac{1}{2}\)

Answer: \(\frac{1}{2}\)

Multiply \(\frac{2}{3} \times \frac{3}{4}\):

\(\frac{6}{12} = \frac{1}{2}\)

Answer: \(\frac{1}{2}\)

Divide \(\frac{5}{6} \div \frac{2}{3}\):

Multiply by reciprocal: \(\frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4}\)

Answer: \(\frac{5}{4}\) or \(1\frac{1}{4}\)

Exercises

Convert \(\frac{17}{5}\) to a mixed number.
[WAEC] Simplify \(\frac{12}{16}\). (Past Question)
Write \(3\frac{1}{2}\) as an improper fraction.
[NECO] Add \(\frac{5}{6} + \frac{1}{3}\). (Past Question)
Subtract \(\frac{7}{8} - \frac{1}{4}\).
Multiply \(\frac{4}{9} \times \frac{3}{2}\).
[JAMB] Divide \(\frac{7}{10} \div \frac{2}{5}\). (Past Question)
Compare \(\frac{5}{12}\) and \(\frac{3}{8}\).
[NABTEB] Write \(\frac{24}{6}\) as a whole number. (Past Question)
Simplify \(\frac{36}{48}\).

Conclusion/Recap

This lesson covered the key concepts of fractions, including types, conversions, simplification, and arithmetic operations. You should now be able to handle problems involving fractions with ease and accuracy.