Use the order of operations: PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

We want to solve what's in the parentheses first.

\(\displaystyle 12\div(1+3)-9\times 6\)

\(\displaystyle 12\div(4)-9\times 6\)

Now, do the division and the multiplication.

\(\displaystyle 12\div 4=3\)

\(\displaystyle 9 \times 6=54\)

Therefore our equation becomes:

\(\displaystyle 3-54\)

Finally, subtract.

\(\displaystyle 3-54=-51\)

Use order of operations, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to solve.

Since there are no parentheses or exponents we can go straight to multiplication and division. 

\(\displaystyle 10 \times 0.5=5\) and \(\displaystyle 18 \div 6=3\)

Therefore the following happens:

\(\displaystyle 36+10\times0.5-18\div6=36+5-3\)

Then add and subtract.

\(\displaystyle 36+5-3=38\)

Using order of operations, we need to solve whatever is in the parentheses first.

\(\displaystyle 9\times8+4-2\div(4-2)=9\times8+4-2\div2\)

Next, do the multiplication and division.

\(\displaystyle 9\times8+4-2\div2=72+4-1\)

Finally, add and subtract.

\(\displaystyle 72+4-1=76-1=75\)

We start with what is inside the parentheses, so \(\displaystyle (1+3)^2-2(4-7)\) becomes \(\displaystyle (4)^2-2(-3)\).

Next, we take care of any exponents, giving us \(\displaystyle 16-2(-3)\).

Next, we take care of multiplication/division, giving us \(\displaystyle 16-(-6)\) or \(\displaystyle 16+6\).

Finally, we carry out our addition/subtraction, leaving us with \(\displaystyle 22\).

Using PEMDAS, we do the parenthetical bit first:

\(\displaystyle 9\times7-(2+6)\div8= 9\times7-(8)\div8\)

Now, we do multiplication and division:

\(\displaystyle 9\times7-(8)\div8=63-1\)

Finally, subtract.

\(\displaystyle 63-1=62\)

This is a classic order of operations question, and if you are not careful, you can end up with the wrong answer!  

Remember, the order of operations says that you have to go in the following order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (also known as PEMDAS).  In this equation, you will start with the parentheses.  In the parentheses, we have 

\(\displaystyle (16\div2^{2})\).

But within the parentheses, you still need to follow PEMDAS.  First, we will solve the exponent, and the square of 2 is 4.  Then, we'll divide 16 by 4, which gives us 4, so we can rewrite our original equation as

\(\displaystyle -10+13-12\div4\).

We can now divide \(\displaystyle 4\) into \(\displaystyle -12\), which gives us

\(\displaystyle -10+13-3\). 

The last step is to add and subtract the numbers above, paying careful attention to negative signs.  In the end, we end up with \(\displaystyle 0\) because \(\displaystyle -10\) added to \(\displaystyle 13\) equals \(\displaystyle 3\), and \(\displaystyle 3\) minus \(\displaystyle 3\) equals \(\displaystyle 0\). 

By the order of operations, in the absence of grouping symbols, multplication must be worked before adding or subtracting. Then the addition and subtraction must be worked in left-to-right order; the subtraction is at left, so the subtraction is worked next, followed by the addition.

By the order of operations, any operations within parentheses must be carried out first; there are two here, the addition and the subtraction. After this is done, the exponent, or squaring, must be worked before the other operations. Squaring, the third operation, is therefore the correct answer.

By the order of operations, in the absence of grouping symbols, the exponent (represented here by cubing) must be worked first. The multiplication must be worked second, followed by the subtraction.