Lesson Notes By Weeks and Term v4 - JHS 2

Lesson Video

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Performance objectives

• Define fractions, decimals, and percentages.
• Convert between these three forms.
• Solve real-life problems using them.
• Compare and order them.
• Simplify and perform basic operations with fractions.

Lesson summary

This lesson revisits the concept of fractions, which are a fundamental part of our daily lives. From sharing a loaf of bread among family members in the morning, to a carpenter measuring wood for a new desk, or a market woman selling half a bag of gari, fractions are everywhere. A strong understanding of how to add, subtract, multiply, and divide fractions is essential for solving everyday problems, for future studies in science and technical subjects, and for managing personal finances. This lesson will strengthen our skills in performing these basic operations and applying them to real-life situations we encounter here in Ghana.

Lesson notes

Part 1: Quick Review of Types of Fractions

A fraction represents a part of a whole. It has two parts: the numerator (the top number) and the denominator (the bottom number). Proper Fraction: The numerator is smaller than the denominator. It is always less than 1. Examples: 1/2, 3/4, 5/8 Improper Fraction: The numerator is greater than or equal to the denominator. It is equal to or greater than 1. Examples: 5/4, 7/3, 8/8 Mixed Number (or Mixed Fraction): A whole number and a proper fraction combined. Examples: 1 ¼, 2 ⅓

Converting Between Improper Fractions and Mixed Numbers Improper to Mixed: Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. Example: Convert 7/3 to a mixed number. 7 ÷ 3 = 2 with a remainder of 1. So, 7/3 = 2 ¹/₃. Mixed to Improper: Multiply the whole number by the denominator and add the numerator. This new number becomes the numerator, and the denominator stays the same. Example: Convert 4 ½ to an improper fraction. (4 × 2) + 1 = 8 + 1 = 9. So, 4 ½ = 9/2. Part 2: Addition and Subtraction of Fractions

Rule: You can only add or subtract fractions that have the same denominator (like denominators). Case 1: Like Denominators Simply add or subtract the numerators and keep the same denominator. Example: 3/8 + 2/8 = (3+2)/8 = 5/8. Case 2: Unlike Denominators You must first find a common denominator. The easiest way is to find the Least Common Multiple (LCM) of the denominators. Example: Solve 2/3 + 1/4. Step 1: Find the LCM of the denominators (3 and 4). Multiples of 3: 3, 6, 9, 12, 15... Multiples of 4: 4, 8, 12, 16... The LCM is 12. Step 2: Convert each fraction to an equivalent fraction with the LCM as the new denominator. For 2/3: How do you get from 3 to 12? Multiply by 4. So, multiply the numerator by 4 as well. (2 × 4) / (3 × 4) = 8/12. For 1/4: How do you get from 4 to 12? Multiply by 3. So, multiply the numerator by 3 as well. (1 × 3) / (4 × 3) = 3/12. Step 3: Add the new fractions. 8/12 + 3/12 = (8+3)/12 = 11/12. Subtracting Mixed Numbers Example: Solve 5 ¹/₄ - 2 ³/₄ Step 1: Convert to improper fractions. 5 ¹/₄ = (5×4+1)/4 = 21/4 2 ³/₄ = (2×4+3)/4 = 11/4 Step 2: Subtract the fractions. 21/4 - 11/4 = (21-11)/4 = 10/4 Step 3: Simplify and convert back to a mixed number if needed. 10/4 = 5/2 = 2 ¹/₂. Part 3: Multiplication of Fractions