Essential of Quant Skills Flashcards
Lowest Common Denominator
Smallest non-zero integer that will divide all
Cross Out
Try to cancel numerator and denominator as much as possible
(a/b)+(c/b)
(a+c)/b
If (a/b)+(c/d)
(ad+bc)/bc -> cross multiple
Cross cancel
works for multiplication and not addition and subtraction and divisions
(a/b)/(c/d)
(ad/bc) -> (outsideoutside)/(insideinside)
Comapring Fractions
Have a reference point (let’s say 1/2) and you say you are more or less than that 1/2
Comapre a/b and c/d
ad > bc
1/(a/b)
b/a -> 1 divided by a fraction is b/a
One way of comapring the fractions
Make all the numerator same > larger denomintor smaller the number (3/2)>(3/4)
Second way of comapring the fractions
Make all the denominator same
Multiplying or dividing both the numerator and denominator by a non-zero
Will not change the value of the fractions
Adding or subtracting the numerator and denominator by a non-zero
Will change the value of the fractions
Fraction between 0 and 1 : adding to the numerator and denominator
make the fraction larger
Fraction between 0 and 1 : subtracting to the numerator and denominator
make the fraction smaller
Fraction greater than 1 : adding to the numerator and denominator
make the fraction smaller
Fraction greater than 1 : subtracting to the numerator and denominator
make the fraction larger if it’s still postive
Decimals
Tenths: 0.1
Hundredths: 0.01
Thousandths: 0.001
To add or subtracts decimals
Line up the decimal points and then add or subtract
To multiply two decimals
1) First ignore the decimals, treat the tow numbers and whole numbers and determine the product
2) Count the total number of the decimals to the rights of the decimals point in the number that were multiplied
3) In the product, move the decimals point to the left the same number of spaces
i. e 15.534*2.8= 4 decimals = 43495200 = 43.4952
Rounding: If the digit to the right is less than 5
keep the digit in the xth place and change everything to the right in the xth place to zero
i.e: 9.746 -> 9.70
If the digit is 5 or greater
round the digit in the xth place up by 1 and change everything to the right of the xth place to a zero
Hundredth : 9.746 -> 9.75
x%
x/100
Convert fraction to a percent
multiply the fraction by 100 and attach the percent sign
Convert decimal or an integer to a percent
Move the decimal point two places to the right and attach the percent sign
i.e: 0.03 = 3%
Convert percent to a decimal
drop the percentage sign and move the decimal point two places to the left
i.e: 0.7% -> 0.007
Converting a terminating decimals
A. 1 decimal : write it over 10 -> 0.3 -> 3/10
B. 2 decimal: write it over 100 -> 1.47
-> 147/100
1/8
- 125
0thers: 3/8 -> 0.125*3
1/2
0.5 ; 50%
1/3
0.333; 33%
1/4
0.25; 25%
1/5
0.2; 20%
1/6
0.167; 16.7%
1/7
0.143; 14.3%
1/8
0.125; 12.5%
1/9
0.111; 11%
1/10
0.1; 10%
Square root of number except for rad 0
Always positive
If b ≠ 0, then (a/b)^2
a^2/b^2
If x ≥ 0 and y >0, then rad(x/y)
rad x/ rad y
If 0
x^2 < x < rad x
Bigger the number, bigger the result when square rooting
0.990^2 > 0.9099^2 > 0.9090^2
Estimation
When estimating, try to round to the whole/ easier #
i.e = (2013^2)/(20.5 199^2) = (2000)^2/(20(200^2)
Perfect square never end in
2
3
7
8
Perfect square end in
0 1 4 5 6 9
Number Line: number on the right
always greater than number on the left
Number line: If the two number are negative
The farther away the number is from the number 0, the small its value and the closer the number is to 0, the larger its value
Comparing the negative fractions
First treat them as normal and switch the sign after you make that change
PEDMAS
Follow PEDMAS and absolute value have the same priority as parentheses and square root also act like parentheses
PEDMAS in fraction
First take care of the top part and then look at the bottom and stuff
Commutative property
a+b = b+a
Associative property
(a+b)+c = a+(b+c)
When we have a sequence of number
add them in any order we want
Commutative property of multiplication
ab = ba
Associative property of multiplication
(ab)c = a(bc)
When we have a sequence of number of multiplication
multiply them in any order we want
Distributive Property of multiplication
a(b+c)= ab+a*c
(b+c)*a
ba+ca
a(b+c+d)
ab+ac+ad
a(b-c)
ab-ac
Common factor
Always be in look out to factor out common factors
Arithmetic tricks
999+578 = 1000+578-1 = 143 1,000,000,000,000-888,888,888,888= 999,999,999,999+1- 888,888,888,888 = 111,111,111,112
0!
1
1!
1
Try to factor out the factorials
11!+10! = 10!(11+1)
