Lesson Notes By Weeks and Term v4 - SHS 1
PROPORTIONAL REASONING
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PROPORTIONAL REASONING
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Subject: Mathematics
Class: SHS 1
Term: 1st Term
Week: 6
Grade code: 1.1.2.LI.2
Strand code: 1
Sub-strand code: 2
Content standard code: 1.1.2.CS.1
Indicator code: 1.1.2.LI.2
Theme: NUMBERS FOR EVERYDAY LIFE
Subtheme: PROPORTIONAL REASONING
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In our daily lives in Ghana, we often deal with parts of a whole. We might share a loaf of sugar bread, divide a plot of family land, or follow a recipe that uses half a cup of gari. Proportional reasoning helps us make sense of these situations. Today, we will explore a powerful tool within this topic: inverses. An inverse is like an "undo" button or an "opposite." Understanding inverses helps us to solve problems where we know a part and need to find the whole, a key skill in everything from cooking to business. For instance, if you know that 2/3 of your money is GHS 10, how do you find the total amount? Inverses give us the key to solve this.
A. The Concept of an Inverse
An inverse is something that reverses or cancels the effect of another thing. In mathematics, we have two main types of inverses we will study today: the additive inverse and the multiplicative inverse. To understand inverses, we must first understand identity elements. Additive Identity: The additive identity is the number that, when added to any number, does not change the number's value. This number is 0. Example: `7 + 0 = 7`, `(-1/2) + 0 = -1/2`. Multiplicative Identity: The multiplicative identity is the number that, when multiplied by any number, does not change the number's value. This number is 1. Example: `15 × 1 = 15`, `(3/4) × 1 = 3/4`. B. Additive Inverse
The additive inverse of a number is the number you must add to it to get the additive identity, 0. It is simply the "opposite" of the number. Rule: To find the additive inverse of a number, just change its sign. If it's positive, make it negative. If it's negative, make it positive.
Example 1: Using a Number Line Imagine you are standing at the point `2/3` on a number line. How many steps must you take, and in which direction, to get back to `0`?