Fractions, LCM and HCF

Grade 7 - Fractions, LCM, and HCF

Lesson Objectives

Understand and work with different types of fractions.
Simplify and perform operations with fractions.
Find the least common multiple (LCM) of numbers.
Determine the highest common factor (HCF) of numbers.
Solve word problems involving fractions, LCM, and HCF.

Lesson Introduction

Fractions, LCM, and HCF are fundamental concepts in everyday mathematics. From sharing a pizza to determining the timing of two flashing lights, understanding these concepts helps solve many real-life problems.

Worked Example

Example 1: Simplify

\frac{12}{16}

.
Divide both numerator and denominator by 4:

\frac{12 \div 4}{16 \div 4} = \frac{3}{4}

Example 2: Add

\frac{2}{5} + \frac{3}{10}

.
LCM of 5 and 10 is 10.

\frac{2 \times 2}{5 \times 2} + \frac{3}{10} = \frac{4}{10} + \frac{3}{10} = \frac{7}{10}

Example 3: Subtract

\frac{5}{6} - \frac{1}{4}

.
LCM of 6 and 4 is 12.

\frac{10}{12} - \frac{3}{12} = \frac{7}{12}

Example 4: Multiply

\frac{3}{7} \times \frac{2}{5}

.
Multiply numerators and denominators:

\frac{3 \times 2}{7 \times 5} = \frac{6}{35}

Example 5: Divide

\frac{5}{8} \div \frac{2}{3}

.
Invert and multiply:

\frac{5}{8} \times \frac{3}{2} = \frac{15}{16}

Example 6: Find LCM of 6 and 8.
Multiples of 6: 6, 12, 18, 24...
Multiples of 8: 8, 16, 24...

\text{LCM} = 24

Example 7: Find HCF of 18 and 24.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

\text{HCF} = 6

Example 8: [WAEC] Find the LCM of 4, 5, and 6. (Past Question)
LCM of 4, 5, and 6 = 60

\text{LCM} = 60

Example 9: Express

\frac{16}{64}

in lowest terms.
Divide by 16:

\frac{16 \div 16}{64 \div 16} = \frac{1}{4}

Example 10: A baker uses

\frac{3}{4}

kg of flour for one cake. How much flour is needed for 5 cakes?

\frac{3}{4} \times 5 = \frac{15}{4} = 3 \frac{3}{4}

Exercises

Simplify $\frac{18}{27}$
Add $\frac{5}{6} + \frac{1}{3}$
Subtract $\frac{7}{8} - \frac{1}{4}$
Multiply $\frac{2}{5} \times \frac{3}{7}$
[NABTEC] Divide $\frac{6}{11} \div \frac{2}{3}$ [Past Question]
[WAEC] Find the HCF of 12, 18, and 30. [Past Question]
[NECO] Find the LCM of 9 and 12. [Past Question]
[JAMB] Simplify $\frac{14}{49}$ to the lowest terms. [Past Question]
A recipe requires $\frac{2}{3}$ cup of oil per dish. How many cups are needed for 6 dishes?
Find the LCM of 15 and 25.

Conclusion/Recap

In this lesson, you've learned how to simplify, add, subtract, multiply, and divide fractions. You also explored how to find the least common multiple and the highest common factor. These are foundational skills useful in many areas of math. In the next lesson, we will explore **Decimal Numbers and Percentages**.