By the end of today, you'll be confident using these tools in everyday Kenyan situations. First, we'll understand rates, ratios, and both direct and inverse proportions. Then we'll solve percentage problems, including profit and loss calculations. Finally, we'll see how these ideas apply to things like market prices, bus fares, and school supplies here in Kenya. Keep your notebooks ready—I'll be pausing for quick checks. If anything feels unclear, just raise your hand, and we'll work through it together. Let's dive in and make these concepts click for you!
Next, let's explore how ratios help us compare quantities in everyday life. A ratio expresses the relationship between two quantities of the same kind, like 2 : 1 meaning for every two parts of one item there is one part of another. Here's a bar chart showing the typical maize‑to‑beans ratio in Kenyan household meals: 2 : 1, 3 : 1, and 4 : 1. Notice how the bars grow as the maize proportion increases. For example, if a meal contains 2 cups of maize and 1 cup of beans, the ratio is 2 : 1. If we double the beans to 2 cups while keeping maize at 2 cups, the ratio becomes 1 : 1, showing a more balanced plate. We can also use ratios to compare class sizes, market prices, or sports scores—any situation where we need to see how one quantity relates to another.
Class, today we'll explore two important ways quantities can be linked – direct and inverse proportions. First, let's look at the key relationships. A direct proportion means that when one value doubles, the other also doubles. An inverse proportion means that when one value goes up, the other goes down. Here we have the direct‑proportion formula y = k·x. For example, if the price per litre of water is 20 shillings, the total cost (y) equals 20 shillings times the number of litres (x). Consider the inverse case: y = k / x. Think of speed and time when traveling a fixed distance – if you go faster, the time needed gets shorter. A Kenyan example: when a group of people shares a water container, the amount of water each person needs (y) decreases as the group size (x) increases – that's an inverse proportion. To recap, direct proportion multiplies a constant, inverse proportion divides by a variable. Keep these formulas handy; we'll use them in later problems.
Let's wrap up what we've learned today with the key take‑aways. First, remember that rates compare different units—like kilometres per hour—while ratios compare quantities with the same unit, such as 3 : 1. Second, direct proportion means both variables move in the same direction; inverse proportion means they move oppositely. Third, percentages turn fractions or decimals into 'per hundred'; for profit percent we use (profit ÷ cost price) × 100. Finally, we applied these ideas to real Kenyan situations—like calculating fuel efficiency, market price changes, and budgeting for school supplies—to see how they work in everyday life. Great job today, everyone! Keep practicing these concepts, and you'll find them handy in many real‑world problems.
