For addition, you use the + symbol e.g. a + b = c:
$$ a + b = c$$
For subtraction, you use the - symbol e.g. a - b = c
$$ a - b = c$$
For multiplication, you just write ab or put a dot in between with \cdot (meaning: “centered dot”) like a \cdot b.
Using a * b doesn't look natural in most cases $a * b$ (but it might make sense sometimes!)
$$a\cdot b = c$$
For fractions, you use \frac{a}{b} or {a \over b}.
You can use a / b if you don't want to make a fraction $a / b$.
$${a \over b} = c$$
For modulo, you can use a \% b if it's. The percent symbol is comment % ... comment ....
Usually in mathematics, you write modulo as “congruence modulo N” which you do like a = b \pmod{N}
$$ a = b \pmod{N}$$
For exponentiation, you use e^{ ... } e.g. e^{i\phi} = \cos(\phi) + i\sin(\phi).
When it's a single variable in the exponent, omitting braces is fine e.g. e^\phi or e^{\phi} are both fine.
$$e^{i\phi} = \cos(\phi) + i\sin(\phi)$$
For logarithm, you use \ln.
$$\ln(1 + x) = 1 + x + $$
For integrals, you use \int, \iint, \iiint, \oint, \oiint, \oiiint.
$$\int \iint \iiint \oint \oiint \oiiint$$