Other Useful Information

  • Every thing has a quantity (the number of) and a denomination (a name).
  • You can only add and subtract things that have the same name (a common denomination).
 
  • The decimal point (.) separates the wholes (on the left side of the decimal) from the parts (on the right side of the decimal).
 
  • The fraction bar (—) separates the numerator (on the top of the fraction) from the denominator (on the bottom of the fraction). The proper name for the fraction bar is “vinculum.”
 
  • The fraction bar also means:
    • the numerator “out of” the denominator.
    • the numerator “per” the denominator.
    • the numerator “divided by” the denominator.
    • the denominator “divided into” the numerator.
 
  • A ratio is a comparison of two numbers by division .
    • Comparing 6 and 8 by ratio gives “6/8 means 6 is three–fourths (¾) of 8.”
 
  • A difference is a comparison of two numbers by subtraction.
    • Comparing 6 and 8 by difference gives “6 is 2 less than 8.”
 
  • A proportion is an equation that says that two ratios are equal.
    • 6/9 = 8/12 is a proportion.
    • This says that 6 and 9 have the same ratio as 8 and 12, since both equal two–thirds (2/3) [6 is two–thirds (2/3) of 9 and 8 is two–thirds (2/3) of 12].
 

The phrase “the quantity” has two meanings:

  • the “amount,” “the quantity of x used is 6 pounds,”
  • the “one composed of the many”...
    • “(2x + 3y)2” is pronounced, “2x plus 3y, the quantity squared.”
    • “2x + 3y2” is pronounced, “2x plus 3y squared.”
  • When multiplying two binomials, learn to “FOIL” mentally, that is, to combine the “OI” mentally and write down just the results.
    • (x + 3)(x + 4) = x2 + 7x + 12 [mentally combine (4x + 3x)] rather than writing down (x + 3)(x + 4) = x2 + 4x + 3x + 12 = x2 + 7x + 12. Learning to do this will save time and will make learning advanced concepts in Algebra II and Pre–Calculus easier.

Be able to apply the Pythagorean Theorem forward and backward.

In a right triangle, a2 + b2 = c2, and a2 = c2 – b2 [and b2 = c2 – a2 ]. This the most often used formula in math and science.

All of the above (b = 0), and 3 + 2i, 5 – 6i (b ≠ 0).

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