A 100% Grade Is 45°, Not 90° | Fractions, Percents and Slope Were Always One Thing

You have seen this sign out on a mountain highway. A triangle with a number in it, and a percent sign next to it. A twelve percent grade. Something is off, though. Percent is what you use for a discount. Why is it bolted to a hill? Fractions, decimals, percents, ratios, rates, slope. We learned these six separately. But we never learned six things. We met the same one thing six times. 📍 Chapters 0:00 The percent bolted to a hill 0:31 We learned it six separate times 0:57 A ratio is not the answer to a division 1:29 Plot the pairs and they line up 2:07 The slope is the ratio 2:53 Why it has six outfits 3:36 So you cannot add them 4:12 Pi was a ratio too 📌 In this episode · A ratio is not the result of a division. It is the relationship between two quantities that move together · Plot every pair with the same ratio and they do not scatter. They land on one straight line through the origin · The slope of that line is the ratio itself (rise ÷ run) · So a 12 percent grade is not an angle, it is a ratio. And a 100 percent grade is not 90 degrees, it is 45 · Take 30 percent off, then 20 percent more, and you did not take 50 percent off. Ratios multiply, they do not add (0.7 × 0.8 = 0.56) · Pi was a ratio all along. Circumference ÷ diameter — which is why circles of every size sit on one line 🔗 The story so far EP.01 Every Number, One Map — Natural to Complex EP.02 Imaginary Numbers Are Not Imaginary EP.03 Euler's Formula Is Just Half a Turn — Mathiter is a math learning app for international school and study-abroad students. Practice that adapts to you → https://mathiter.com #math #ratio #proportion #percent #slope #fractions #middleschoolmath #mathexplained