Resource that teaches everything about fractions

Question

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.

please help!

Answer 1

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.

And about compound fractions:

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.

Answer 2

Too long for a comment…

It is well worth forgetting the “sum of fractions” formula because it is not a fact about fractions - simply a consequence of the other facts. To experts in fractions this sounds unnecessary, but this extra formula that needs remembering, with its seemingly magic multiplications, is a great stumbling block to the uninitiated.

Rather than saying $$\frac a b + \frac c d = \frac {ad+cb}{bd}$$

say simply $$\frac a e+ \frac c e = \frac {a+c}e$$

• that is, give the obvious answer to the “same denominator” case and give no answer at all to the question “what is the sum of two fractions with different denominators?”

Given that we also know that $\frac a b=\frac {ax}{bx}$, you can work out $\frac a b + \frac c d$ for yourself by multiplying top and bottom of the first fraction by something and top and bottom of the second fraction by something, in such a way that the bottoms of both fractions are the same.

Of course this is exactly equivalent to the magic formula with $bd$ in the denominator, but it is a lot less confusing to say “I can do this” rather than “this memorised magic works but I don’t know why”.