Arithmetic
Some notes on doing arithmetic with a pen and some paper.
Lexicon
prime number: a whole number above 1 that can't be made by multiplying other whole numbers
composite number: a whole number above 1 that can be made by multiplying other whole numbers
factors: the numbers you multiply together to get x
multiple: what you get after mutiplying x by another factor
prime factorization: is finding which prime numbers multiply together to make the original number
reciprocal: like flipping a number, x to 1/x, 1/x to x
Addition
(COMING SOON)
Subtraction
To subtract numbers with more than one digit, write down the larger number first and the smaller number directly below it, making sure to line up the columns! Then do subtractions one column at a time.
47
- 12
----
35
Regrouping
(COMING SOON)
Multiplication
(COMING SOON)
Division
Divisibility Tests
A number is divisible by...
- 2 if it has an even ones digit.
- 3 if the sum of it's digits is divisible by 3.
- 4 if the number named by it's last two digits is divisible by 4.
- 5 if it's ones digit is 0 or 5.
- 6 if it's ones digit is even and the sum of it's digits is divisible by 3.
- ...ya know what, just try dividing by 7.
- 8 if the number named by it's last three digits is divisible by 8.
- 9 if the sum of it's digits is divisible by 9.
- 10 if it's ones digit is 0.
Fractions
Find Decimal Notation
In most cases, you should just divide the top of the fraction by the bottom.
Sometimes, it will be easier to use the method below:
- Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.
- Multiply both top and bottom by that number.
- Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)
Find Percentage Notation
First, find decimal notation. Then, find that decimal's percentage notation.
Decimals
Find Fractional Notation
First, write the decimal down like so:
0.75
0.75 >>> ----
1
Then, multiply both top and bottom by 10
for every number after the decimal point.
0.75 75
---- >>> ----
1 100
Find Percentage Notation
Just move the decimal point 2 places to the right, in order to multiply by 100:
0.75 >>> 75%
0.03 >>> 3%
4.00 >>> 400%
Ratios
(COMING SOON)
Percentages
Find Decimal Notation
Just move the decimal point 2 places to the left, in order to divide by 100:
75% >>> 0.75
3% >>> 0.03
400% >>> 4.00
Find Fractional Notation
75
75% >>> ----
100
NOTE: If the percentage isn't a whole number, multiply the fraction by a power of 10.
Exponents
Multiply something by itself.
2^1 = 2
2^2 = 2 * 2 = 4
2^3 = 2 * 2 * 2 = 8
2^4 = 2 * 2 * 2 * 2 = 16
To multiply or divide something with an exponent, you just add or subtract the exponents.
a^2 * a^5 = a^7
b^4 / b = b^3
Logarithms
Get the power used in an exponent.
log(16, 2) = 4