This problem aims to find an** algebraic expression** for a given **verbal expression**, using the knowledge of simple mathematics and some commonly known algebraic and arithmetic techniques.

This kind of problem requires the understanding of the **keywords** that are used in mathematics as a way to express **algebraic terminology**. Similarly, some problems are so designed that they require verbal expressions such that an algebraic expression is already given.

A **verbal expression** is a simplified interpretation of a condition using mathematical terms. It determines the associations and measures that arise in quantities, for example, the difference of three times a number, $y$, and two.

## Expert Answer

So in this problem, we are going to understand how to shift a **verbal expression** or equation into an algebraic expression or equation. When shifting verbal expressions into mathematical expressions, we utilize **keywords** or **keyphrases** to specify the operation that can be used. Distinct keywords or phrases included in the verbal expression let us to also decide the order of numbers or variables, such as “**less than or equal to**“, “**greater than or equal to**”, “**more than**”, and “**difference of**”.

The keyword * more than a number* suggests that the arithmetic operation of

**addition**, which is usually indicated by the plus symbol $+$, is going to be used in this problem. Likewise, we are already given a number $6$ which is going to be incremented by a variable $c$. So, the verbal expression $6$ more than the number $c$ can be expressed as the algebraic expression $ 6 + c $.

These kinds of expressions are commonly used in** word problems**, where you must examine the distinctive words that specify the operation required to solve the problem.

## Numerical Result

The required **expression** is $ 6 + c $.

## Example

Write an algebraic expression for the given **verbal expressions**.

**–**$6$**less than**any arbitrary positive number.**–**$10$**more than**the**product**of $5$ and the positive number $b$.**–**$4$**divided by**the**summation**between a number $a$ and $7$.

For the** first part**, let $a$ represent the unknown positive number. The keyphrase **less than **indicates the arithmetic operation of **subtraction**. So, the verbal expression $6$ less than the positive number $a$ can be composed as the algebraic expression $ 6 – a $.

For the **second part**, we are given a number $b$. The keyphrase **more than **indicates the arithmetic operation of** addition**, and the phrase **product **indicates **multiplication**. Hence, the verbal expression $10$ more than the product of $5$ and the positive number $b$ can be expressed as the algebraic expression $ 5b + 10 $.

For the **third part**, we are again given a number $a$. The key phrase **is divided by** points to the arithmetic operation of **division**, and the phrase **summation **indicates addition. So, the verbal expression $4$ divided by the summation between the number $a$ and $7$ can be composed as the algebraic expression $ \dfrac{4} {a + 7} $.