Fractions and Decimals

Grade 7 Math - Fractions and Decimals

Lesson Objectives

Understand the concept of fractions and decimals.
Convert between fractions and decimals.
Perform addition, subtraction, multiplication, and division with fractions and decimals.
Apply fractions and decimals in real-life problem solving.
Develop confidence in handling fractional and decimal numbers.

Lesson Introduction

Have you ever shared a pizza with friends and thought about what fraction of the pizza you got? Or have you gone shopping and noticed prices like $3.75? Fractions and decimals are everywhere! Today, you’ll learn how to work confidently with them.

Core Lesson Content

Understanding Fractions:

A fraction represents a part of a whole. It has a numerator (top number) and a denominator (bottom number).

Understanding Decimals:

A decimal is another way of representing parts of a whole, especially when dealing with powers of 10.

Conversion between Fractions and Decimals:

You can divide the numerator by the denominator to convert a fraction to a decimal.

Worked Examples

Example 1: Convert $\frac{3}{4}$ to decimal.

Divide numerator by denominator:

3 \div 4 = 0.75

Example 2: Convert $0.6$ to fraction.

Write as $\frac{6}{10}$ and simplify:

\frac{6}{10} = \frac{3}{5}

Example 3: Add $\frac{2}{5}$ and $\frac{1}{3}$ .

Find LCM of 5 and 3 = 15.

\frac{2}{5} = \frac{6}{15},\quad \frac{1}{3} = \frac{5}{15}

Add:

6 + 5 = 11

\frac{11}{15}

Example 4: Subtract $0.8 - 0.45$ .

0.8 - 0.45 = 0.35

Example 5: Multiply $0.7 \times 0.5$ .

0.7 \times 0.5 = 0.35

Example 6: Divide $0.9 \div 0.3$ .

0.9 \div 0.3 = 3

Example 7: Simplify $\frac{5}{8} + \frac{7}{16}$ .

Find LCM = 16.

\frac{5}{8} = \frac{10}{16}

10 + 7 = 17

\frac{17}{16} = 1\frac{1}{16}

Example 8: Find the product of $\frac{3}{7} \times 0.6$ .

0.6 = \frac{3}{5}

\frac{3}{7} \times \frac{3}{5} = \frac{9}{35}

Example 9: Divide $\frac{5}{6} \div \frac{2}{3}$ .

Keep first fraction, flip second and multiply:

\frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = 1\frac{1}{4}

Example 10: Convert $3.75$ into a fraction.

3.75 = \frac{375}{100} = \frac{15}{4}

Exercises

Convert $\frac{5}{8}$ to decimal.
Convert $0.25$ to a fraction.
Simplify: $\frac{3}{5} + \frac{2}{3}$ .
Subtract: $0.9 - 0.45$ .
Multiply: $0.25 \times 0.4$ .
Divide: $0.8 \div 0.2$ .
[WAEC] Add $\frac{7}{10}$ and $\frac{2}{5}$ . (Past Question)
[NECO] Convert $1.2$ to fraction. (Past Question)
[NABTEC] Divide $\frac{4}{9} \div \frac{2}{3}$ . (Past Question)
[JAMB] Simplify $\frac{7}{8} + \frac{5}{16}$ . (Past Question)

Conclusion/Recap

Today, you learned how to work with fractions and decimals confidently: converting, adding, subtracting, multiplying, and dividing them. In the next lesson, we will explore the topic of percentages!