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### Course: Algebra (all content)>Unit 1

Lesson 5: Writing algebraic expressions introduction

# Writing expressions

Learn to write algebraic expressions in and out of word problems.

## Why do we have math if we can describe things in words?

Sometimes in math we describe an expression with a phrase. For example, the phrase
"$2$ more than $5$"
can be written as the expression
$2+5$.
Similarly, when we describe an expression in words that includes a variable, we're describing an algebraic expression (an expression with a variable).
For example,
"$3$ more than $x$"
can be written as the algebraic expression
$x+3$.
But why? Why use math if we can describe things in words? One of the many reasons is that math is more precise and easier to work with than words are. This is a question you should keep thinking about as we dig deeper into algebra.

## Different words for addition, subtraction, multiplication, and division

Here is a table that summarizes common words for each operation:
OperationWordsExample algebraic expression
Additionplus, sum, more than, increased by$x+3$
Subtractionsubtracted, minus, difference, less than, decreased by$p-6$
Multiplicationtimes, product$8k$
Divisiondivided, quotient$a÷9$
For example, the word "product" tells us to use multiplication. So, the phrase
"the product of $8$ and $k$"
can be written as
$8k$.

## Let's take a look at a trickier example

Write an expression for "$m$ decreased by $7$".
Notice that the phrase "decreased by" tells us to use subtraction.
So the expression is $m-7$.

## Let's try some practice problems!

### Basic expressions

Write an expression for "$y$ more than $7$".

Write an expression for "$6$ minus $b$".

Write an expression for "$x$ divided by $9$".

Write an expression for "$2$ multiplied by $t$".

Write an expression for "the sum of $a$ and $4$".

### More complicated expressions

Write an expression for "$8$ less than the product of $7$ and $x$".

Write an expression for "the sum of $6$ and the product of $3$ and $d$".

### Word problems

Daniel makes $100$ dollars each week. He worked for $x$ weeks this summer.
How much money did Daniel make this summer?

Sebastian has $12$ more trophies than Megan. Megan has $t$ trophies.
How many trophies does Sebastian have?

## Want to join the conversation?

• I have a problem with sentence problem like this:Write an expression for "
8
less than the product of
7
and
x
". and I wrote 8-7x but they gave me wrong how I can answer that ?
• because it says "8 less than", that means that 8 is supposed to be subtracted from whatever part of the expression is after it, so the answer would be 7x-8. i hope this helped. :)
• Why do you talk in this ducument that 3 more than x is x+3? It should be3+x
(1 vote)
• Because of the commutative property of addition "x+3" and "3+x" mean exactly the same thing. Both are acceptable translations of the phrase.
• How do I solve this problem 8 squared
• I have a weird problem, when I practiced on khan on subtraction with algebra it showed something like this p - 6 I use that example to do my subtraction problem on IXL but it said it was wrong I had to put the number then the letter.
(1 vote)
• "p - 6" and "-6 + p" are equivalent and it shouldn't matter which term comes first. The commutative property of addition tells use the 2 expressions are identical. However, you may have been given some explicit directions in IXL that asked you to write the terms in a certain order. If you didn't follow their instructions, that could have caused it to be wrong.

The other possibility is that you confused "p - 6" with "-6p". The first one is subtraction. The second one is multiplication. These are different.

Hope this helps.
• These were some pretty easy questions. The problem is that its very confusing for which order I should put the problem in.
(1 vote)
• What is this? Is this in High School. I've got 3 years till High School
(1 vote)
• But this is just the easy part of algebra 1
(1 vote)
• This stuff is pretty easy but i can never be too sure. That is why i'm going back to the basics of it to learn it again and improve my skills
(1 vote)
• I'ts pretty easy once you you learn the system and the patterns that were put into the problems.
(1 vote)
• anyone know what m decreased by 200 is?
(1 vote)
• At what is the answer to 51 less than x squared?
(1 vote)