Lesson Notes By Weeks and Term v4 - JHS 3

Lesson Video

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Performance objectives

• Add and subtract fractions.
• Multiply and divide fractions.
• Convert between fractions, decimals, and percentages.
• Solve real-world problems with fractions.

Lesson summary

This lesson focuses on combining the four basic mathematical operations (addition, subtraction, multiplication, and division) on fractions. In our daily lives in Ghana, we often deal with parts of a whole – sharing a loaf of bread, dividing a piece of land, or calculating profits from a small business. This lesson is crucial because real-life problems are rarely simple; they often require multiple steps. By mastering how to combine these operations using the BODMAS rule, learners will be equipped to solve more complex, practical problems accurately.

Lesson notes

Part 1: Quick Revision of Basic Operations with Fractions

Before we combine operations, let's quickly remember how to perform each one. Addition and Subtraction: To add or subtract fractions, they must have a common denominator. Find the Least Common Multiple (LCM) of the denominators. Convert each fraction to an equivalent fraction with the LCM as the new denominator. Add or subtract the numerators only. Keep the common denominator. Simplify the result if possible. *Example:* `2/3 + 1/4` -> LCM of 3 and 4 is 12. -> `(8/12) + (3/12)` = `11/12`. Multiplication: This is the most straightforward operation. Multiply the numerators together. Multiply the denominators together. Simplify the result. (You can also simplify by cross-cancelling before multiplying). *Example:* `3/5 × 2/7` = `(3×2) / (5×7)` = `6/35`. Division: To divide by a fraction, we multiply by its reciprocal (we flip it). We use the "Keep, Change, Flip" (KCF) method. Keep the first fraction. Change the division sign (÷) to a multiplication sign (×). Flip the second fraction (find its reciprocal). Multiply the fractions as normal. *Example:* `1/2 ÷ 3/4` -> `1/2 × 4/3` = `(1×4) / (2×3)` = `4/6`, which simplifies to `2/3`. Part 2: The Order of Operations - BODMAS

When a problem has multiple operations, we cannot just solve it from left to right. We must follow a specific order to get the correct answer. This order is given by the acronym BODMAS. B - Brackets: Always solve any calculation inside brackets first. `( )` O - Of: This means multiplication. It is often used with fractions, e.g., "1/2 of 1/4". D - Division: Perform any division. `÷` M - Multiplication: Perform any multiplication. `×` A - Addition: Perform any addition. `+` S - Subtraction: Perform any subtraction. `-`

Important Rule: Division and Multiplication have the same priority. If you have both, solve them from left to right. Similarly, Addition and Subtraction have the same priority. Solve them from left to right. Part 3: Combining Operations with Fractions using BODMAS