Math: ratios: making oatmeal: 4:9
Self-tutoring about ratios: the tutor reflects about preparing oatmeal. The ratio of oatmeal to water, with the brand I use, is 1 and 1/3 cup to 3 cups. As such, it’s a less convenient ratio to scale up or down …
Category: math
Metric system: how big is a hectare?
Tutoring science, the metric system may arise. The tutor mentions the definition of a hectare. hectare (noun): a square unit spanning 10000m2. A hectare can be pictured an as area 100m wide by 100m long. Another way to imagine a …
Calculator usage: negative numbers to rational exponents (with odd roots)
Tutoring high school math, scientific calculators are a permanent fascination. The tutor mentions a quirk many might share. Due to and the fact that a common exponent notation is xa=x^a, it follows that (-8)^(2/3)=4. Curiously, of all the calculators in …
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Spreadsheets: Excel: the pi() function
Tutoring math, your curiosity naturally extends to spreadsheets. The tutor points out a neat feature of Excel. If you type =pi() in a cell, the value of π will appear. I find that 14 decimal places are available. Source: www.math.com …
Math, engineering, trades: steepness measurement: definition of grade
Tutoring math, you encounter grade. The tutor discusses its definition and why it might be surprising. Grade is defined as 100%*(vertical/horizontal). In the above diagram, it would be as follows: grade=100%*(rise/run). By itself, rise/run is called slope. Therefore, grade=100%*slope What …
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Math: commutative operations
Tutoring math, you encounter definitions. The tutor defines commutative. commutative adj describes an operation for which the order of the inputs doesn’t change the output. Since 6×7=7×6, multiplication is commutative. So is addition. Source: Gallian, Joseph A. Contemporary Abstract Algebra. …
Math: what does associative mean?
Tutoring math, you mention definitions. The tutor defines associative. associative(adj): independent of grouping: for instance, (a+b)+c = a+(b+c), meaning that addition is associative. Multiplication is associative as well. Source: Gallian, Joseph A. Contemporary Abstract Algebra. Toronto: D.C. Heath and Company, …
Math: minimum sum of squares
Tutoring math, you encounter patterns. The tutor brings up one about sums of squares. If two whole numbers sum to a constant even one, then their minimum sum of squares will come from each being half. The reason: Let the …
Math: counting: how many ways can four whole numbers sum to 10?
Tutoring math, you might be asked counting problems. The tutor brings up one. How many solutions can be found to x1 + x2 + x3 + x4 = 10, where x1, x2, x3, and x4 are all whole numbers? Imagine …
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Psychology, probability: a parking game
Tutoring probability, you can imagine so many everyday examples. The tutor shares one. This morning I went to pick up some groceries. I like to load groceries through the rear door of the van. However, I also like to drive …