Write Expression to represent
unknown quantity
Sometimes, you find yourself having to write out your own algebraic expression
based on the wording of a problem.
In that situation, you want to
1. read the problem carefully,
2. pick out key words and phrases and determine their equivalent
mathematical meaning,
3. replace any unknowns with a variable, and
4. put it all together in an algebraic expression.
The following are some key words and phrases and their translations:
Addition: sum, plus, add to, more than, increased by, total
Subtraction: difference of, minus, subtracted from, less than, decreased by,
less
Multiplication: product, times, multiply, twice, of
Division: quotient divide, into, ratio
Write the phrase as an algebraic expression.
The sum of a number and 10.
It looks like the only reference to a mathematical operation is the word
sum - so what operation will we have in this expression? If you said addition,
you are correct!!!
The phrase 'a number' indicates that it is an unknown number - there was no
specific value given to it. So we will replace the phrase 'a number' with the
variable x. We want to let our variable represent any number that is unknown
Putting everything together, we can translate the given english phrase with
the following algebraic expression:
The sum of a number and 10
*'sum' = +
*'a number' = variable x
Let’s try another!
Write the phrase as an algebraic expression.
The product of 5 and a number.
Again, we are wanting to rewrite this as an algebraic expression, not
evaluate it.
This time, the phrase that correlates with our operation is 'product'
- so what operation will we be doing this time? If you said
multiplication, you are right on.
Again, we have the phrase 'a number', which again is going to be
replaced with a variable, since we do not know what the number is.
Let’s see what we get for this answer:
The product of 5 and a number
*'product' = multiplication
*'a number' = variable x
Write the phrase as an algebraic expression.
3 less than twice a number
First of all, we have the phrase 'less than' which mathematically
translates as subtraction. You need to be careful with this phrase, it
is very tempting to start off with 3 and put your subtraction sign after
the 3. However, think about it, if you want 3 less than something, you
are 3 below it. In order to be 3 below something, you would have to
subtract the 3!!! So you would not have 3 minus, but minus 3 as PART
of your expression.
The other part of the expression involves the phrase 'twice a number'.
'Twice' translates as two times a number and, as above, we will replace
the phrase 'a number' with our variable x.
Putting this together we get:
3 less than twice a number
*'less than' = *'twice' = 2 times
*'a number' = variable x