LambLamb

(-7) + (-15) = (-22)

(-7) * 22/7 = (-22)

\(\frac{-9}{17}*2\frac{8}{13}\) = -9/17 *34/13 = -306/ 221 = -1 85/221 or 1 5/13 or 1.384615...

\(-\frac{306}{221}\) or  \(1\frac{5}{13}\) or 1.384615...

30 cm³ = 0.00003m³

The conversion of cm to meters is 100:1.

But that's cubed, see.

So the ratio of cm³ to cubic meters is 100³:1, or 1,000,000:1

Take 30 cm³, divide it by the conversion factor for m³, and voila.

30cm³ /1,000,000 = 0.00003 m³

8 * 1/2 does not mean the same thing as \({8}^{1/2}\)

An exponent of 1/2 is the same as taking the square root. And the square root of 8 is \(2\sqrt{2}\).

\({81}^{1}\)

\({3}^{4}\)

and

\({9}^{2}\)

Of course, all of these use only integers.

There are infinitely many other combinations of (rational and) irrational bases and exponents that equal 81.

The calculator on this website will tell you much more quickly than I can!

But if you'd like to learn how to do it, then here it goes:

When dividing a fraction, you are actually multiplying by the reciprocal. (A reciprocal is a "flipped" fraction, example, reciprocal of 44/90 is 90/44)

Instead of 3/4 ÷ 4/5, you would be doing 3/4 * 5/4. 

When multiplying fractions, multiply the top numbers together and multiply the bottom numbers together.

3/4 * 5/4 = 15/16, or 0.9375

Hope this helps!

To prove a number is irrational, you could assume that it can represented by a ratio of integers and then prove that would be a contradiction if that were to happen.

For example with \(\sqrt{2}\), you could assume it can be represented by a ratio of integers, but if you tried to do that, you'd find that one of the integers would have to be both odd and even at the same time, which is a contradiction, proving \(\sqrt{2}\) is irrational.

All square roots of non perfect squares are irrational by a version of this proof.

All an irrational number is is a number which cannot be represented as a ratio of integers and has no repeating patterns in its infinitely continuing decimal expansion.

There's probably more on this topic, but I can't really go any deeper right now.

2 19/30

or 79/30

Hope this helps!

Try it out!

if a= 5, b = 7, and c = 13,  then

a/b/c = 5/7/13 = 5/91

ac/b = 5*13/7 = 65/7

5/91 does not equal 65/7

Since one case proves the identity wrong, the whole thing must be wrong. So you can conclude:

a/b/c does not equal ac/b

Hope this helps!

3/8 + 2/16

The calculator on this website will tell you directly, but ...

to add fractions, the denominators (bottom numbers) must be the same. To make 8 the same as 16, it's pretty easy, jsut multiply by 2.

So multiply the fraction by 2/2 to get 6/16. (2/2 = 1, so the value of the fraction does not change)

then just add numerators (top numbers)

6/16 + 2/16 = 8/16.

That answer is not wrong, but you can simplify it to 1/2.

Hope this helps!!