How do you express the phrase "Five more than the product of 7 and a" as an algebraic expression?

Question

71307 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-19T23:26:32

$7 a + 5$ $7a + 5$

The word product refers to multiplication, so the product of 7 and a is $7 a$ $7a$

Five more would mean addition of 5 to the value.

$7 a + 5$ $7a +5$

Answer 2 · 2018-05-19T23:43:55

$7 \times a + 5$ $7timesa+ 5$ , also written as $7 a + 5$ $7a+5$ .

We need to break down the phrase into its math parts.

We start with:

$Five more than the product of 7 and a$ $"Five more than the product of 7 and "a$

"Five" means the number 5.
So "Five more than" means "5 added to something".

That something must be what's left: "the product of 7 and $a$ $a$ ."
So, we are taking the product of 7 and $a$ $a$ , and then adding 5 to it.

Our phrase is now:

$[the product of 7 and a] + 5$ $["the product of 7 and "a]" " + 5$

In math, the word "product" means "the result of multiplying." To get a product, we need (at least) two things to multiply together.

The remaining part of our phrase tells us what to multiply together: 7 and $a$ $a$ .

In math, "the product of 7 and $a$ $a$ " is what you get when you multiply "7 times $a$ $a$ ", also written as $7 \times a$ $7xxa$ .

Our phrase is now:

$[7 \times a] + 5$ $[7 xx a] + 5$

We can clean this up a bit by using $7 a$ $7a$ instead of $7 \times a$ $7 xx a$ :

$7 a + 5$ $7a+5$

Let's double check. This math phrase should mean the same as "five more than the product of 7 and $a$ $a$ ".

$7 a$ $7a$ is indeed the product of 7 and $a$ $a$ , and $+ 5$ $+5$ indicates "five more than" that product.

So yes, $7 a + 5$ $7a+5$ is "five more than the product of 7 and $a$ $a$ ".