Melody

example

$$215*98\approx 200*100\approx 20,000$$

A km is much bigger than a mm so there will be a lot less of them so you will be dividing.

$$\div\;\by\;\;1000\;\;to\;get\;metres\\\\ then\\\\ \;\;\div \;\;by\;1000\; again\; to\;get\;km$$

SO IT DOES!    ARN'T YOU CLEVER.     

If               1         is      70%

then        1/7        is     10%

s0      (1/7*3) must be 30%

You cannot solve it Tenacious because there is no equal sign :)

The asker want to expand and simplify it.

(3x+5)(3x-5)

you can expand it the long way but you should learn to recognise this as the difference of 2 squares.

The brakets are the same but one has a minus and the other a plus.  (Thay are a conjugate pair)

the answer will be      $$(3x)^2-5^2=9x^2-25$$

Thanks Tenacious, you are right there are a number of methods   

You calc method is good but you actually do not need the inside brackets because division is done before addition.   BUT if you are not sure then it is always a good idea to add the brackets.

(1+(2/5)*5 = (1+2/5)*5

$$\\1\frac{2}{5}*5\\\\
=\frac{5*1+2}{5}*\frac{5}{1}\\\\
=\frac{7}{5}*\frac{5}{1}\\\\
=\frac{7}{\not{5}}*\frac{\not{5}}{1}\\\\
=7$$

Thanks Ang2061,

Good effort ang but not quite right    (I'll give you 3 points for your participation  )

$$\\(\frac{1}{3})9^3\\\\
=\frac{1}{\not{3}}\times \not{9}^3*9*9\\\\
=3*81\\\\
=243$$  

Could you explain a little how you did that anon please?

Thank you Heureka and thankyou anons for voicing your concerns.   

If you want to learn effectively you MUST speak up.    

This is always a source of confusion.   

Firstly

$$\\-4^2=-1*4^2=-1*16=-16\\
$Where as $\\
(-4)^2=-4*-4=+16\\\\
$Now why is this so?$\\
consider\\
50-3^2=50-9=41\\
$ See how the minus sign DID NOT belong to the 3$\\
$If it did belong to the 3 then this would be how it had to be done$\\\\
50+(-3)^2=50+9=59 = 50+3^2\\\\$$

Now I do not think that anyone would think    $$50+3^2$$     should equal   $$50-3^2$$

so the minus sign cannot belong to the 3       

Thanks Geno - I never would have thought to do that !