Fraction / Decimals / Conversions

Question 1

Complex Numerator Shortcut?

Answer 1

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.

Question 2

Properties of Zero (2)

1. If the numerator = 0,
2. If denominator = 0,

Answer 2

1. If numerator is 0, the fraction = 0

2. If denominator is 0, fraction is undefined.

Question 3

Proper Fractions / Decimals:

Basic Math Principles (4)

Multiplying

Squaring

Dividing

Square Root

Answer 3

1. Multiplying by a PF = smaller value
2. Squaring = smaller
3. Dividing by PF = larger
4. Square Root = larger

Question 4

Reciprocals:

1. What are they?
2. How to get reciprocal of two independent terms?
3. How do you get rid of a fractional coefficient?

Answer 4

1. ) two numbers, whose product = 1
   
   • Fractions can have more than one reciprocal
2. ) Combine the terms and flip
3. ) Multiply by reciprocal ON BOTH SIDES

Question 5

Properties of Numerators and Denominators

Numerator / Denominator increase vs decrease

Answer 5

Numerator = value increase

Denominator = value decrease

increase equally is closer to 1

decrease equally is away from

Question 6

Comparing Fractions (4)

Answer 6

1. Cross-multiply (whichever is greater = greater fraction)
2. Approximate –> if fractions are large ID ≈ equivalents)
3. Convert to decimals –> memorize conversion chart!
4. 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)

Question 7

Converting Fractions into Decimals (3)

Answer 7

1. Conversion chart
2. Denominator to power of 10
3. If denominator = 2’s & 5’s it will terminate.

Question 8

How do you convert repeating decimals?

What determines if decimal will repeat or terminate?

Answer 8

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.

Question 9

Consecutive Zeros to left or right of the Decimal

eg) If k = 2^7 x 5^4…how many zeros will k have?

Answer 9

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!

Question 10

Multiplying Decimals

Answer 10

Swing product back equal number of spots.

Question 11

Decimal Place Values

Answer 11

8, –– Thousands
2 –– Hundreds
1 ––Tens
3, –– Units 
.
6 –– Tenths
5 –– Hundredths
4 –– Thousandths

Question 12

How do you determine # of zeros to the right

Answer 12

–– Count 10’s; multiply remainders:

>10 = no zeros // >100 = 1 zero