5 times the sum of a number and 8

Answer 1

Hello Erfan!

Are you asking how to express that algebraically?

If so, then here is what I think you are looking for!

So first, we want to translate "five times a number and eight" into algebra.

We know what 5 is, and we know what 8 is, so the only thing we don't know is "a number".

When we don't know a value, we often assign it a variable/name.

So let's represent it with a variable. Let's call it n, for number. (x is also fine)

Next, let's think about what order the operations are going to be applied.

It says "5 times a number and eight".

Does this mean five times a number, and then add 8? or five times (a number and 8)?

The way English works it should be "(five) times (a number and 8)"

In other words, determine what a number and 8 is, and then multiply that by 5.

Alright, nice.

Let's think about what it means by "a number and 8".

Hmm.. What is 2 and 3? 5 right? So here "and" must mean addition.

Let's translate this into algebra.

We decided to call "a number" n since we didn't know what it is, right?

so we have "n and 8", which means addition, so we end up with:

"n + 8".

Sweet! Awesome. Now we need five times this value.

We want 5 times the whole number n + 8, so we need to use parentheses.

5 * (n + 8)

So we have 5 times a number and eight!

If you are not familiar with the order of operations, there is a useful mnemonic:

PEMDAS : Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.

Some people memorize it by reciting "Please Excuse My Dear Aunt Sally".

Basically, we evaluate expressions from left to right and do things with Parenthesis first, and then exponents, and then multiplication, then division, etc, as we go from left to right.

So for example:

4 * 5 + 2

would be evaluated as so:

Multiplication is done first based on our above PEMDAS ordering, going from left to right

So we have 4* 5 = 20

Then addition, so we 20 + 2 = 22.

If we did not have this order of operations you might be tempted to do:

4 * 5 + 2 =??

Well, 5 + 2 = 7

so

4 * 7 = 28.

Clearly this is different, and is not what is intended. So order of operations is really important, and this is why we had to include parenthesis in the above expression of

5 * (n + 8).

Otherwise we might end up with

5 * n + 8 which is "8 and five times a number"

not "five times a number and 8"

I hope this helps!