In the first section, we only looked at very basic expressions such as "four more than a number" or "the product of x and y."

Sometimes, though, we'll be dealing with more complicated expressions that require us to think carefully about our use of order of operations. Just a reminder - parentheses come first, followed by exponents, followed by multiplication and division, followed by addition and subtraction.

When we convert words to an algebraic expression, we may need to insert some parentheses here and there, to make sure that things get done in the proper order.

For example, consider the following: "The sum of 5 and x, times 11"

The sum of 5 and x is 5 + x, and times means multiplication, so you might be tempted to write:

5 + x · 11

But let's stop to think about this; our order of operations rules tell us that we should do multiplication first. But if we do that, we're no longer summing 5 and x! So we need parentheses to show that we do the addition first:

(5 + x) · 11

Here's another example: "five less than x, times five more than x".

Again, you might be tempted to write:

x - 5 · x + 5

Because that's the order things appear in the phrase. But order of operations tells us that in the expression above, we would do 5 · x first, and that's wrong. This time we need to use two sets of parentheses, since there is both an addition and a subtraction that needs to happen before the multiplication:

(x - 5) · (x + 5)

One more example: "the sum of 5 and twice x." In this example, we don't need any parentheses. Why? Because we would write this as:

5 + 2x

And the order of operations says the multiplication happens first, and that's what we wanted!

For each question below, write an algebraic expression. Remember that since these are expressions (not equations) you shouldn't have an equals sign!