Fractions, Decimals and Percentages

Week 4: Fractions, Decimals and Percentages

Class: JSS1 | Subject: Mathematics | Term: First Term

Learning Objectives

By the end of this lesson, students should be able to:

• Define and classify fractions (proper, improper, mixed)
• Perform operations on fractions (addition, subtraction, multiplication, division)
• Convert between fractions, decimals, and percentages
• Apply fractions and percentages to real-life situations

What is a Fraction?

A fraction represents a part of a whole. It is written as a/b where 'a' is the numerator (the part we have) and 'b' is the denominator (the total number of equal parts). The denominator can never be zero.

Types of Fractions

• Proper Fractions: The numerator is less than the denominator. Examples: 2/5, 3/7, 1/4. Value is less than 1.
• Improper Fractions: The numerator is greater than or equal to the denominator. Examples: 7/3, 5/2, 9/4. Value is greater than or equal to 1.
• Mixed Numbers: A whole number and a proper fraction combined. Examples: 2 and 1/2, 3 and 3/4, 5 and 1/3.

Converting Improper Fraction to Mixed Number: 7/3 = 7 divided by 3 = 2 remainder 1 = 2 and 1/3

Converting Mixed Number to Improper Fraction: 3 and 3/4 = (3x4 + 3)/4 = 15/4

Equivalent Fractions

Equivalent fractions are different fractions that represent the same value. We create them by multiplying or dividing both numerator and denominator by the same non-zero number.

Example: 1/2 = 2/4 = 3/6 = 4/8 = 5/10

Addition and Subtraction of Fractions

To add or subtract fractions, they must have the same denominator. If they don't, find the LCM of the denominators.

Example 1: 2/5 + 3/5 = 5/5 = 1

Example 2: 3/4 + 2/3
LCM of 4 and 3 = 12
3/4 = 9/12, 2/3 = 8/12
9/12 + 8/12 = 17/12 = 1 and 5/12

Example 3: 5/6 - 1/4
LCM of 6 and 4 = 12
5/6 = 10/12, 1/4 = 3/12
10/12 - 3/12 = 7/12

Multiplication of Fractions

Multiply numerators together and denominators together. Simplify the result if possible.

Example: 3/4 x 2/5 = 6/20 = 3/10

Example: 2 and 1/2 x 1 and 1/3 = 5/2 x 4/3 = 20/6 = 10/3 = 3 and 1/3

Division of Fractions

To divide by a fraction, multiply by its reciprocal (flip the second fraction).

Example: 3/4 divided by 2/5 = 3/4 x 5/2 = 15/8 = 1 and 7/8

Decimals

A decimal is another way to represent fractions. The decimal point separates the whole number part from the fractional part. Each position after the decimal point represents a power of 1/10.

Example: 3.457 = 3 + 4/10 + 5/100 + 7/1000

Converting Fractions to Decimals

Divide the numerator by the denominator.

3/4 = 0.75, 1/3 = 0.333... (recurring), 2/5 = 0.4

Percentages

A percentage (%) means "per hundred" or "out of 100." It is a way of expressing a fraction with a denominator of 100. Percentages are widely used for discounts, interest rates, exam scores, and statistics.

Fraction to Percentage: Multiply by 100%. Example: 3/4 x 100% = 75%

Percentage to Fraction: Divide by 100. Example: 45% = 45/100 = 9/20

Decimal to Percentage: Multiply by 100. Example: 0.65 = 65%

Percentage to Decimal: Divide by 100. Example: 82% = 0.82

Conversion Summary

Fraction to Decimal: Divide numerator by denominator
Decimal to Percentage: Multiply by 100
Percentage to Fraction: Write over 100, then simplify
Fraction to Percentage: Multiply by 100%

Word Problems

Problem 1: A class has 40 students. If 60% are girls, how many boys are there?
Girls = 60% of 40 = 24. Boys = 40 - 24 = 16 boys.

Problem 2: A shirt costs N5,000. With a 15% discount, sale price = 5,000 - 750 = N4,250.

Problem 3: Amina spent 3/4 of her pocket money on books and 1/8 on snacks. Remaining = 1 - 7/8 = 1/8.

Evaluation Questions

• 1. Simplify: 2/3 + 5/6 - 1/4
• 2. Calculate: 3 and 1/2 x 2 and 2/3
• 3. Convert 7/8 to a decimal and a percentage
• 4. A farmer sold 35% of his 200 goats. How many goats remain?
• 5. Express 0.375 as a fraction in its lowest terms

Summary

Fractions, decimals, and percentages are three different ways of expressing parts of a whole. Being able to convert between them is a vital mathematical skill. Fractions are useful for exact calculations, decimals for measurement, and percentages for comparison and everyday use. Mastering operations with fractions and understanding their relationship with decimals and percentages is essential for success in mathematics.