Download Translating Verbal Expressions into Mathematical Expressions

The Test of Reasonableness
In general applying a test of reasonableness to an answer means looking at it in relation to the numbers operated upon to
determine if it’s “in the ballpark.” Put in simple terms, you look at the answer to see if it makes sense. For example, if you determine
10% of $75 to $750, you should immediately notice something is very wrong, because 10% of something is much smaller than the
original amount.
The test of reasonableness comes very much into play in word problems. For example, questions asking for length, dollars, or
time should never give negative answers because those things would not make sense if they were negative (what is -3 feet?). Also,
think about what the answer should be. If I invest $400 dollars in a bank at 8% interest for 3 years, I would expect the balance to be
larger than the original amount that I invested (that’s why we put money in the bank!), so an answer that is smaller than $400 is
obviously wrong.
Translating Verbal Expressions into Mathematical Expressions
Verbal Expressions
added to
more than
the sum of
increased by
the total of
Examples
6 added to y
8 more than x
the sum of x and z
t increased by 9
the total of 5 and y
Math Translation
6+y
8+x
x+z
t+9
5+y
minus
less than
subtracted from
decreased by
the difference
between
x minus 2
7 less than t
5 subtracted from 8
m decreased by 3
the difference between y and 4
x-2
t-7
8-5
m-3
y-4
10 times 2
one half of 6
the product of 4 and 3
10 X 2
(1/2) X 6
4X3
multiplied by
y multiplied by 11
11y
Division
divided by
the quotient of
the ratio of
x divided by 12
the quotient of y and z
the ratio of t to 9
x/12
y/z
t/9
Power
the square of
the cube of
squared
the square of x
the cube of z
y squared
x
3
z
2
y
Equivalency
equals
is
is the same as
1+2 equals 3
2 is half of 4
½ is the same as 2/4
1+2 = 3
2 = (½)X4
yields
represents
3+1 yields 4
y represents x+1
3+1 = 4
y=x+1
greater than
less than
greater than or equal
to
at least
no less than
less than or equal to
at most
no more than
-3 is greater than -5
-3 > -5
-5 is less then -3
-5 < -3
x is greater than or equal to 5 x ≥ 5
Addition
Subtraction
Multiplication times
of
the product of
2
1
2

2
4
Comparison
x is at least 80
x is no less than 70
x is less then or equal to -6
y is at most 23
y is no more than 21
x ≥ 80
x ≥ 70
x ≤ -6
y ≤ 23
y ≤ 21
Solving Application Problems
Problem-Solving Strategy:
1) Analyze the problem. What are you trying to find? What’s the given info?
2) Work out a plan before starting. Draw a sketch if possible. Look for indicator words (e.g. gained, lost,
times, per) to know which operations (+,-, x,÷) to use.
3) Estimate a reasonable answer.
4) Solve the problem.
5) Check your work. If the answer is not reasonable, start over.
Example:
Each home in a subdivision requires 180 ft of fencing. Find the number of homes that can be fenced with 5760
ft of fencing material.
1) What are we trying to find? Total number of homes that can be fenced.
Given info: 5760 ft of material, 180 ft of fencing per home.
2) Work out a plan. We want to know how many homes can be fenced with 5760 ft of fencing. If we divide
180 feet per home into 5760 feet we will get the total number of homes ( The feet units cancel out).
3) Estimate a reasonable answer.
Round 5760 to 6000 and 180 to 200.
6000÷200 = 30
4) Solve the problem. See below.
5) Check your work.
Check division. Does 32x18=5760 ? Yes.
Is 32 close to our estimate, 30? Yes.
So our answer is 32 homes. (Make sure the units “homes” is in the answer!)
5760 ft 
1 home 5760

 32 homes
180 ft
180
32
180 5760
- 540
360
- 360
0