Complex Numerator Shortcut?
Split the fraction to simplify addition or subtraction.
eg: y-x/x = y/x - x/x = y/x - 1
Note: denominators can NEVER be split.
Properties of Zero (2)
- If the numerator = 0,
- If denominator = 0,
- If numerator is 0, the fraction = 0
2. If denominator is 0, fraction is undefined.
Proper Fractions / Decimals:
Basic Math Principles (4)
Multiplying
Squaring
Dividing
Square Root
- Multiplying by a PF = smaller value
- Squaring = smaller
- Dividing by PF = larger
- Square Root = larger
Reciprocals:
- What are they?
- How to get reciprocal of two independent terms?
- How do you get rid of a fractional coefficient?
- ) two numbers, whose product = 1
- Fractions can have more than one reciprocal
- ) Combine the terms and flip
- ) Multiply by reciprocal ON BOTH SIDES
Properties of Numerators and Denominators
Numerator / Denominator increase vs decrease
Numerator = value increase
Denominator = value decrease
increase equally is closer to 1
decrease equally is away from
Comparing Fractions (4)
- Cross-multiply (whichever is greater = greater fraction)
- Approximate –> if fractions are large ID ≈ equivalents)
- Convert to decimals –> memorize conversion chart!
- Pick a litmus –> determine what’s bigger/smaller than the litmus fractions & utilize above 3 methods between the two groups.
CONVERSION CHART: 1/3= .3 (repeating) 1/6 = .16̅ 1/7 = .14 1/8 = .125 1/9 = .1 (repeating) 1/11 = .09 (repeating) 1/99 = .01 (repeating)
Converting Fractions into Decimals (3)
- Conversion chart
- Denominator to power of 10
- If denominator = 2’s & 5’s it will terminate.
How do you convert repeating decimals?
What determines if decimal will repeat or terminate?
Convert by setting equal to x; multiply decimal out by a power of 10.
(# of zeros = length of repeating sequence)
2’s and 5’s terminate.
Consecutive Zeros to left or right of the Decimal
eg) If k = 2^7 x 5^4…how many zeros will k have?
Zeros come from 2’s and 5’s, thus, count the number of 10s…
More advanced Q’s make you count 2’s and 5’s
eg) If k = 2^7 x 5^4…how many zeros will k have?
2^4 + 5^4 = 4 zeros!
Multiplying Decimals
Swing product back equal number of spots.
Decimal Place Values
8, –– Thousands 2 –– Hundreds 1 ––Tens 3, –– Units . 6 –– Tenths 5 –– Hundredths 4 –– Thousandths
How do you determine # of zeros to the right
–– Count 10’s; multiply remainders:
>10 = no zeros // >100 = 1 zero
