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

May 19, 2018

$7 a + 5$

#### Explanation:

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

Five more would mean addition of 5 to the value.

$7 a + 5$

May 19, 2018

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

#### Explanation:

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

$\text{Five more than the product of 7 and } a$

"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 $a$."
So, we are taking the product of 7 and $a$, and then adding 5 to it.

Our phrase is now:

["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 $a$.

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

Our phrase is now:

$\left[7 \times a\right] + 5$

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

$7 a + 5$

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

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

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