GoldenLeaf

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6+(8+3^2)-3(11-2(6-(8-6)))+1

Here's some nice PEMDAS here~

Parenthesis

We have:

(8+3^2)

and

(11-2(6-(8-6)))

Inside the parenthesis, we apply PEMDAS again:

(8+3^2) ---> (8+9)

and

(11-2(6-(8-6))) ---> (11-2(6-2))

Again:

(8+9) ---> 17

and

(11-2(6-2)) ---> (11-2(4))

Again:

(11-2(4)) ---> (11-8)

Again:

(11-8) ---> 3

And now, we have done almost everything in parenthesis. Insert the final answers from each part taken out back in the place of the parts in parenthesis.

6+(17)-3(3)+1

There are no exponents to deal with now.

Multiplication and Division

3(3) ---> 9

Addition and Subtraction

6+17-9+1

6 + 17 = 23 - 9 = 14 + 1 = 15

Your final answer is 15

The area will be 180 cm^2

Because you're changing both length and width, you're making each side 3x bigger than it originally was. We can then take the scale to the width (3) and the scale to the length (3) and multiply those together.

(20 cm^2)*(3*3) = 20*9 = 180

To double-check:

4*5 = 20 ---> (4*3)*(5*3) = 12*15 = 180 

2*10 = 20 ---> (2*3)*(10*3) = 6*30 = 180 

Find the molar mass of Iron

55.845 g/mol

Take the 5.5g (what you have) and put it in the numerator

Take the 55.845g/mol (molar mass) and put it in the denominator

$${\frac{{\mathtt{5.5}}}{{\mathtt{55.845}}}} = {\mathtt{0.098\: \!486\: \!883\: \!337\: \!81}}$$

There are 0.098 moles in 5.5g of Fe (iron)

7/(1/4)

Okay, since we can't divide by a fraction, we will have to make the fraction a whole number. The easiest way to do this is to treat the numerator and denominator as seperate parts and multiply both top and bottom by the reciprocal of the fraction: In this case, that number is 4.

(7*4)/((1/4)*4) = 28/1

Since any number over 1 is itself... (28/1 = 28) ...the answer is 28.

Think of it this way: If you take nothing from nothing in an equal amount of nothing, all you had to begin with was nothing 

The answer, in this case, would be zero.

$${\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$

Think of the fractions as added onto the whole numbers. Take the equation and add the whole numbers together. Separate the fractions.

$$\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right){\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)$$

3+2 is 5, but what about 1/2 + 1/3? To add fractions, find the LCM, or Least Common Multiple.

2: 2, 4, 6, 8, 10...

3: 3, 6, 9, 12, 15...

The first number where these two have the same factor is 6, so, in order to add these numbers together, make the denominators of both 6. For 1/2, we pultiply the top and the bottom by 3, and for 1/3 we multiply both by 2.

(1*3)/(2*3) = 3/6

(1*2)/(3*2) = 2/6

Now, since they have a common denominator, add the numerators together:

$${\frac{{\mathtt{3}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{6}}}} = {\frac{{\mathtt{5}}}{{\mathtt{6}}}} = {\mathtt{0.833\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

Final answer: 5 5/6

(Another method of finding the LCM is to multiply the two numerators: In this case, multiplying 2 and 3:

$${\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}} = {\mathtt{6}}$$

In the end, the answer is still 6.

From there, you can then multiply one factor's denominator by the other's and vice versa. After that, proceed as normal.)

metre = metre...?

so an equal ratio

Each kilometre is equivalent to 1000 metres. Since there are 2.4 kilometres, a simple ratio can find the answer.

$${\mathtt{2.4}}{km}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{1\,000}}{m}}{{\mathtt{1}}{km}}}\right)$$

Multiply:

$${\frac{{\mathtt{2.4}}{km}{\mathtt{\,\times\,}}{\mathtt{1\,000}}{m}}{{\mathtt{1}}{km}}}$$

The km (kilometres) cancel out and from there it is simple multiplication.

$${\frac{{\mathtt{2.4}}{\mathtt{\,\times\,}}{\mathtt{1\,000}}}{{\mathtt{1}}}} = {\mathtt{2\,400}}$$