 # Write an algebraic expression for: 6 more than a number c.

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.

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 $\dfrac{4} {a + 7}$.