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Ratio and proportion (College Math I).pptx
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- 3. Direct Proportion: • Twoquantities are in direct proportion when they increase or decrease in the same ratio. • For example, if 12 cans of milk have a mass of 4 kg, then 24 cans of milk will have a mass of 8 kg • i.e., if the quantity of cans doubles then so does the mass • If cost of 2 pens is 10 rupess then cost of 5 pens will be ……?
- 4. Real life examplesof Direct Proportion: H.W: Write another 3 examples of direct proportion??
- 6. Example: Charles’s lawstates that for a given mass of gas at constant pressure, the volume is directly proportional to its thermodynamic temperature. A gas occupies a volume of 2.4 liters at 600 K. Determine a) the temperature when the volume is 3.2 liters b) the volume at 540 K
- 7. Inverse Proportion • Inverseproportion means that, as the value of one variable increases, the value of another decreases, and that their product is always the same. • For example, the time for a journey is inversely proportional to the speed of travel. • So, if at 30 m.p.h. a journey is completed in 20 minutes, then at 60 m.p.h. the journey would be completed in 10 minutes. • Double the speed, half the journey time. • Note that 30 × 20 = 60× 10 • Two variables, x and y, are in inverse proportion to one another if y is proportional to 1/ x , y α 1 𝑥 • or y = k x or k = x y where k is a constant, called the coefficient of proportionality.
- 8. In another example, Thetime needed to dig a hole is inversely proportional to the number of people digging. So, if 4 men take 3 hours to dig a hole, then 2 men (working at the same rate) would take 6 hours. Half the men, twice the time. (Note that 4 × 3 = 2 × 6.)