# Write an algebraic expression for the following: 1) the quotient of a number and 0.76, increased...

## Question:

Write an algebraic expression for the following:

1){eq}\; {/eq} the quotient of a number and {eq}0.76 {/eq}, increased by {eq}6.5 {/eq}

2){eq}\; {/eq} the product of a number cubed and the sum of {eq}57.6 {/eq} and {eq}3.42 {/eq}

## Algebraic Expressions:

Translating words into algebraic expressions is no simple task. Each sentence is structured differently and needs to be taken case by case. Typically, it is useful to break apart the sentence by "and" which can indicate a sum, a product, a quotient, or a difference. To the left of the "and" is the first term of the operation and the right is the second. This can help group the sentence as one would with parentheses in a mathematical expression.

1. Let {eq}x {/eq} represent the unknown number. Translate each part of the sentence as follows:

"the quotient of a number and 0.76" {eq}\implies ~ \frac{x}{0.76} {/eq}

"increased by 6.5" {eq}\implies ~ \frac{x}{0.76} + 6.5 {/eq}

giving the algebraic expression

{eq}\frac{x}{0.76} + 6.5 {/eq}

2. Again, let {eq}x {/eq} represent the unknown number. Break down the sentence to then translate each part as follows:

"a number cubed" {eq}\implies ~ x^3 {/eq}

"the sum of 57.6 and 3.42" {eq}\implies ~ 57.6 + 3.42 {/eq}

"the produce of a number cubed and the sum of 57.6 and 3.42" {eq}\implies ~ x^3 \cdot (57.6 + 3.42) {/eq}

giving the algebraic expression

{eq}x^3 \cdot (57.6 + 3.42) {/eq}