# Using all types of fractions

Is their a website that teaches you everything you need to know about fractions, just fractions.

I ask this because I do calculus...and I suck at fractions. I hate them so much. I have no idea how to manipulate them in equations or do anything. Especially compound fractions. I've never been taught fractions outside of rote learning equations.

• The Wikipedia page may be more helpful than you might suspect. – David H Jul 26 '14 at 13:05
• once you have $\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}$ and $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$, you basically have everything – John Fernley Jul 26 '14 at 13:08
• maybe $1/\frac{a}{b}=\frac{b}{a}$ is good to be confident with? – John Fernley Jul 26 '14 at 13:09
• oh and $\frac{ac}{bc}=\frac{a}{b}$ of course. This ought to be an answer – John Fernley Jul 26 '14 at 13:10
• This book and the wikipedia page explain everything you need. – user5402 Jul 26 '14 at 13:47

All you need to know about fractions:

Trivia $$\frac0A=0$$ $$\frac AA=1$$ $$\frac A0\text{ is forbidden}$$

**Sum and difference**$$\frac AB\pm\frac CD=\frac{AD\pm BC}{BD}$$ **Product**$$\frac AB\cdot\frac CD=\frac{AC}{BD}$$ **Quotient**$${\frac AB}:{\frac CD}={\frac AB}\div{\frac CD}={\frac AB}/{\frac CD}=\frac{\frac AB}{\frac CD}=\frac{AD}{BC}$$ **Power**$$\left(\frac AB\right)^\alpha=\frac{A^\alpha}{B^\alpha}$$ Fractions can be simplified when you see a common factor:

Simplification $$\frac{AB}{CB}=\frac AC\frac BB=\frac AC$$ but this is something you already knew from the second relation.

Composition $$A\frac BC=\frac A1+\frac BC=\frac{AC+B}C$$ but this is something you already knew from the first relation.
Decomposition $$\frac AB=Q\frac RB,$$ where $Q$ is the quotient of the integer division of $A$ by $B$, and $R$ is the remainder.
• It should also be noted that the mixed fraction notation $A\frac{B}{C} = \frac{A}{1} + \frac{B}{C}$ is ambiguous with the multiplication $A\frac{B}{C} = \frac{A}{1} \times \frac{B}{C} = \frac{AB}{C}$. Mixed fractions are rarely used and should be discouraged. – LucasVB Jul 26 '14 at 13:34
• In actual usage, the notation $A\frac BC$ means a mixed fraction exactly when $A$, $B$ and $C$ are all bare numbers. If any of them is a variable or an arithmetic expression, then it means a product. So when one evaluates, for example, $2\frac{2+2}5$ step by step, one needs to careful to write the next step as $2\cdot\frac{4}{5}$ rather than $2\frac45$ to avoid suddenly writing something that will be read as a mixed fraction. – hmakholm left over Monica Jul 26 '14 at 13:43
• Also for trivialities don't forget to assume that $A\neq0$ in your two first properties. – Hakim Jul 26 '14 at 13:45