Fractions/Decimals/Precents

Question 1

Digits/Decimals

Answer 1

clean up decimals as (Integer * Power of 10)
f.e., 0.0034 = 34 * 10^4

Units digit patterns
Ends in 0, 1, 5, or 6? Stays same forever.
Ends in 4 or 9? Powers of 4 end in 4 or 6 / Powers of 9 end in 9 or 1, based on whether exponent is odd or even.

Ends in 2, 3, 7 or 8? Goes through a cycle of four numbers.
Powers of 2 (2, 4, 8, 6) …
Powers of 3 (3, 9, 7, 1) …
Powers of 7 (7, 9, 3, 1) …
Powers of 8 (8, 4, 2, 6),

figure out how far exponent is from a multiple of 4.

Question 2

Fractions

Answer 2

Question 3

Percents

Answer 3

Question 4

Ratios

Answer 4

• Use “Multiple of ____ “ thinking a lot, or you might be fooled. Most ratio
  problems have an implied integer constraint, so if you have a ratio of boys
  to girls that is 5 to 11, think “Boys are a multiple of 5. Girls are a multiple of
  11. The total is a mult of 16.”
• Scale It Up (Write ratio horizontally and add a “Total” column). A real #
  for any of the pieces, or for the sum or difference between any of the
  pieces, allows us to solve for the multiplier and figure out all the real
  values.
• Combine Multiple Ratios
  When you have two separate ratios, think about the piece that’s common
  to both ratios. Scale both ratios up until the common piece is the same.
• Old Ratio -> New Ratio
  1. write Old and New as two fraction equations, then solve system
  2. use unknown multiplier for Old, set up one fraction equation for the New.
  3. or Backsolve