For these types of problems remember this acronym to help with the order of operations (The order of operations is just a way of saying, the order in which you do stuff in math problems)

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Where you do each operation in order down the list. If they are the same operation back to back without any of the above operations in the way(such as 8*2*3) you can do them in any order (In the case of 8*2*3 you could do 8*2 = 16 then 16*3 = 48, or 2*3 = 6 then 6*8 = 48)

Explanation aside, here is our problem!

67 * 6.8 *

First let’s take care of the

Square roots are pretty simple. They are the inverse operation (the operation which is the opposite thus undoing it… example addition’s inverse operation is subtraction) of squaring. Squaring is taking one number and multiplying it by itself. Square roots are simply the opposite. You take one number (the one under the square root) then find the one numbers which multiplied by itself equals our number under the square root. Example: = 2, because 2^2 = 4. If you want you can think of it like if you take the number you found, like in the case of = 2. And square it (multiply it by itself) You should get the same number underneath the sign. Hence 2^2 (2*2) = 4.

Now we need to ask a question, what ONE number that is multiplied by itself equals our number, 9.

Let’s figure out some squares!

1^2 = 1*1 = 1

2^2 = 2*2 = 4

3^2 = 3*3 = 9

Looks like we found our number.

= 3

67 * 6.8 * 3

If you are allowed to use a calculator then use it here, otherwise keep following along.

6.8 is awkward to use. So let’s make it a fraction!

Start with the decimal 0.8:

0.8 = 8/10 (That’s because it is in the tenths place… so 8 tenths which is 8/10)

Now we need the 6 part.

Make 6 have 10 as a denominator by multiplying it by 10/10.

6 * (10/10) = 60/10

Add the numerator (the tops) together!

60 + 8 = 68

68/10 is our final fractional number

We can rewrite the whole multiplication problem like this:

Let’s get the two bigger numbers multiplied together!

67*68

I’m going to break this multiplication problem down into parts added together. You can what I’m about to do, because multiplication is just an extension of addition. (refer to the picture for all the multiplication and division)

As I mentioned at the bottom, dividing by 10 is equivalent to moving the decimal point over to the left by 1. The number of times you move the decimal to the left is equivalent to the number of zeroes 1 has to the right of it. In the case of 100 you move it to the left 2 times. In the case of 1,000,000 you move the decimal to the left 6 times. If you are multiplying by 10 instead of going to the left the decimal goes to the right. If there is nothing there like in the case of 9*10, you place a zero there. 9*10 = 90. In the case of non decimal numbers the number of zeroes next to 1 is equivalent to the number of zeroes the number you are multiplying by will gain.

Refer to the picture for the work, but here is the answer:

67 * 6.8 * = 1366.8