Math Flashcards
What is 2 squared?
4
What is 3 squared?
9
What is 4 squared?
16
What is 5 squared?
25
What is 6 squared?
36
What is 7 squared?
49
What is 8 squared?
64
What is 9 squared?
81
What is 10 squared?
100
What is 11 squared?
121
What is 12 squared?
144
What is 13 squared?
169
What is 14 squared?
196
What is 15 squared?
225
What is 1 cubed?
1
What is 2 cubed?
8
What is 3 cubed?
27
What is 4 cubed?
64
What is 5 cubed?
125
What is 6 cubed?
216
What is the trick when figuring out the number of zeros when taking a square root in the answer?
ex. square root of (0.00000025)
CUT THE ZEROS IN HALF!!!!
0.0005
If you square (0.006) = 0.000036
DOUBLE THE ZERO’S
In a fractions problem (say 1/3 and 1/4) what is the best picking number that you could choose?
Least common denominator
ie. 3 x 4 = 12 would be the best choice for this problem
What is the conversion of feet to miles?
5280 feet / mile
Explain the communtative laws of addition and multiplication
a + b = b + a
a x b = b x a
Explain the associative law of addition and multiplication
(a + b) + c = a + (b + c)
(a x b) x c = a x (b x c)
Explain the distributive law
a (b + c) = ab + ac
What is the order of operation and how is it easy to remember?
Please _E_xcuse _M_y _D_ear _A_unt _S_ally
Parentheses
Exponents
Multiplication
Division (together from L to R)
Addition
Subtraction (together from L to R)
How do you multiply fractions?
num x num
den x den
3/4 x 9/7 = 27/28
How do you divide fractions?
1/5 / 4/11 = 1/5 x 11/4 = 11/20
flip the bottom fraction then multiply
How do you add fractions?
need to have the same denominator, then add
How do you add and subtract mixed numbers?
subtract or add the integer out front, then add or subtract the fractions
if the fraction would be a negative number, take from the integer prior to adding or subtracting
ex. 4 5/8 - 2 7/8
fraction: 13/8 - 7/8 = 6/8 = 3/4
Integer: 3 - 2 = 1
Answer = 1 3/4
Explain a ratio
part / part that add up to the whole
what is the fraction for 0.0001
1 / 10,000
what is the fraction for 0.111
111 / 1000
Change 0.564 into a fraction
564 / 1000 (divide by 4) = 141 / 250
Explain the division of decimals
It’s easiest to discuss division of decimals if expressed in fraction form
ex. 4.15 divided by 32.2 = 4.15 / 32.2
step 1: make both, numerator and denominator whole numbers
4.15 / 32.2 x 100 = 415 / 3220 = 0.12
Explain the process of multiplying two expressions in scientific notation.
ex. (1.1 x 10^6) (5 x 10^17) = ?
Simply multiply the coefficients and add the exponents to find answer
(1. 1 x 10^6) (5 x 10^17)
1. 1 x 5 = 5.5
10^(6+17) = 10^(13)
answer = 5.5 x 10^(13)
Explain the process of dividing two expressions in scientific notation.
ex. (6.2 x 10^5) / (2.0 x 10^-7)
Simply divide the coefficients and subtract the exponents
(6. 2 x 10^5) / (2.0 x 10^-7)
6. 2 / 2 = 3.1
10^(5 - -7) = 10^12
answer = 3.1 x 10^12
Explain when a number is in scientific notiation and raised to an exponent
ex. (6.0 x 104)2
the coefficient is raised to that exponent, and the original exponent is multiplied by that exponent
(6.0 x 104)2
62 = 36
(104)2 = 108
answer = 36 x 108
= 3.6 x 10<span>9</span>
Explain adding or subtracting numbers expressed in scientific notation
ex. (3.7 x 10^4) + (1.5 x 10^3)
They must have the same exponent, when they do not, the appropriate conversion must be made first
(3.7 x 10^4) + (1.5 x 10^3)
(37 x 10^3) + (1.5 x 10^3)
= 38.5 x 10^3
= 3.85 x 10^4
Explain how to turn a fraction into a percent
ex. 3/5 to percent = ?
3/5 = 3/5 x 100
= (3x100)/5 %
= 3 x 20 %
= 60%
What is the conversion from fraction, decimal, percent:
3/4
3/4 = 0.75 = 75%
What is the conversion from fraction, decimal, percent:
2/3
2/3 = 0.666 = 66 2/3%
What is the conversion from fraction, decimal, percent:
1/3
1/3 = 0.333 = 33 1/3%
What is the conversion from fraction, decimal, percent:
1/4
1/4 = 0.25 = 25%
What is the conversion from fraction, decimal, percent:
1/5
1/ 5 = 0.2 = 20%
What is the conversion from fraction, decimal, percent:
1/6
1/6 = 0.167 = 16.7%
What is the conversion from fraction, decimal, percent:
1/7
1/7 = 0.143 = 14.8%
What is the conversion from fraction, decimal, percent:
1/8
1/8 = 0.125 = 12.5%
What is the conversion from fraction, decimal, percent:
1/9
1/9 = 0.111 = 11.1%
What is the conversion from fraction, decimal, percent:
1/10
1/10 = 0.1 = 10%
What is the conversion from fraction, decimal, percent:
1/20
1/20 = 0.05 = 5%
What is the percent formula?
ex. if percent is 60% and part is 12, what is whole?
percent = part / whole
or
part = whole x percent
ex. 12 / 60% = 20 is whole
Explain what the following means:
“What percent of …A… is(are) …B…?
A = whole number
B = part
B / A = %
Explain the percent increase/decrease formula
% increase = (amount of increase) / (original #) x 100
% decrease = (amount of decrease) / (original #) x 100
New whole = original whole +/- amount change
Ex. if a number increases from 50 to 70, what is the percent increase?
70 - 50 = 20
20 / 50 x 100 = 2 / 5 x 100
= (2 x 100) / 5
= 2 x 20 = 40%
Explain if, x is n% greater than y
then x is (100 + n)% of Y
ex. if x is 10% greater than y, then x is 110% of y
Explain if, x is n% less than y
then x is (100 - n)% of Y
ex. if x is 70% less than y, then x is 30% of y
What is the formula for computing average
average = (sum of the terms) / (# of terms)
Explain how you can use the average to find the sum
sum = (average) x (# of terms)
ex. if average = 50 of 10 numbers, the sum is ?
sum = 50 x 10 = 500 total sum
Explain how you find a missing number?
ex. if the average is 7 of 4 numbers, the numbers are 3, 5, and 8, what is the fourth number?
- To find the missing number when you’re given the average, use the sum
ex. average = sum / total #
sum = avg x total # = 7 x 4 = 28
total of the three given numbers = 3, 5, 8 = 16
28 - 16 = 12 = fourth number
Explain the basic logarithms property formula
Properties of logs are dependant on the Law of exponents
“The lagarithm of x to the base b”
logb(x) = c ; then bc = x
What is:
log4(16) = c
log<span>10</span>(10000) = c
log25(5) = c
log5(x) = 3
logb(36) = 2
log10(100) = c
log4(16) = 2
log<span>10</span>(10000) = 4
log25(5) = 1/2
log5(x) = 3 x = 125
logb(36) = 2 b= 6
log10(100) = c c = 2
Properties of logs
Explain the product of two in a logarithm
The logarithm of the product of two numbers equal the sum of the individual logarithms
logb(s x t) = logb(s) + logb(t)
Properties of logs
Explain the quotient of two in a logarithm
The logarithm of the quotient of two numbers equal the numerator minus the logarithm of the denominator
logb (s / t) = logb(s) - logb(t)
Properties of logs
Explain the logarithm of a power with a positive base
Exponent of the power muliplied by the logarithm of the base of that power
logb(sp) = p x logb(s)
Explain the answer to the following log base 10
log10(0.01) = ?
log10(0.1) = ?
log10(1) = ?
log10(10) = ?
log10(100) = ?
log10(1000) = ?
An increase of one logarithmic unit (in base 10) corresponds to a muliplication of 10 of the actual total
log10(0.01) = -2, since 10-2 = 0.01
log10(0.1) = -1, since 10-1 = 0.1
log10(1) = 0, since 10<span>0</span> = 1
log10(10) = 1, since 10<span>1</span> = 10
log10(100) = 2, since 10<span>2</span> = 100
log10(1000) = 3, since 10<span>3</span> = 1000
How many integers are between:
-2 3/4 to 1 1/4
4
include 0 as an integer
