# Translation of Multi-Part Math Phrases into Algebraic Expressions

In our previous lesson ( Basics of Writing Algebraic Expressions ), we went over some simple examples of writing algebraic expressions because they only involve a single operation. This time, we will deal with math phrases that are a bit more complex. The algebraic expressions here may contain **two or more operations**. The basic keywords that we learn before will serve as the foundation as we work on with the more challenging math phrases to interpret into algebraic expressions.

Don’t worry, this lesson will go over enough examples so that you will have more opportunities to see them in action.

## Examples of How to Translate Multi-Part Math Phrases into Algebraic Expressions

**Example 1**: Write an algebraic expression for the math phrase ” *3 more than twice a number*“.

* Solution*: To make this much easier to understand, we are going to divide this phrase into two parts. First, recognize that we have an unknown number. We can represent it by any letters of the alphabet. Let the unknown number be the variable

*The diagram below should help us see what’s really going on.*

**x.**If you think about it, there is an unknown number represented by variable * x* that is being doubled or multiplied by 2. Whatever is the product, we will add 3 to it. So, our final answer should look like the one below.

**Example 2**: Write an algebraic expression for the math phrase ” the difference of half a number and 10″.

* Solution*: Suppose the variable

*is the unknown number. The keyword “difference” prompts us that we are going to perform subtraction. It is crucial here that we pay attention to the order of subtraction. After the word “difference”, we should expect two quantities. The first one will be the minuend, while the second one will be the subtrahend. Take a look at the diagram below.*

**y**Referring to the diagram above, we will subtract the first quantity by the second quantity. In other words, the second quantity is subtracted from the first quantity. The final answer for math phrase should like something like this,

**Example 3**: Write an algebraic expression for the math phrase ” 7 less than the product of a number and 6″.

* Solution*: We know that “less than” suggests a subtraction operation. But we need to be a little bit careful here because the order on how we subtract is important. Suppose the unknown number is represented by the variable

*. Let’s put this on a diagram to make a sense of it.*

**k**Actually, this math phrase can be rewritten as

” *the product of a number and 6 minus 7 *“

The “7 less than” means “minus 7” to whatever quantity being described which in this case “the product of a number and 6”. Here’s the final interpretation of the math phrase in an algebraic expression:

**Example 4**: Write an algebraic expression for the math phrase ” the average of a number and 4″.

* Solution*: To get started on this particular math phrase, we need to review what the word “average” means. To calculate

**average**or

**mean**of two or more numbers, we will need to add up all the numbers to get a sum then divide it by the number of entries or how many numbers there are. If we let

*be the variable to represent the unknown number, the math phrase above can be expressed in algebraic expressions as,*

**m****Example 5**: Write an algebraic expression for the math phrase ” the quotient of 1, and 1 decreased by a number”.

* Solution*: The keyword “quotient” means we will divide. In this case, we want to divide the number

**1**by the quantity

**. Below is the algebraic expression that can represent the math phrase above. Let**

*1 decreased by a number**be the unknown number.*

**a****Example 6**: Write an algebraic expression for the math phrase ” a third of the square of a number, increased by 2″.

* Solution*: There are few things going on here. First, the part of the phrase which states ”

*a third of the square of a number*” can be interpreted as ”

*the square of a number divided by 3*“. We will need to raise the unknown number by 2 then divide by 3. Suppose the unknown number is

*, we get –*

**t**We are not done yet. The last step to do is to add the quantity above by 2 to incorporate the remaining part of the phrase ” *increased by 2* “. So here’s the final representation of the given math phrase.