Step-by-step explanation:
wordsalgebraic symbolsreason
two decreased by a number 2 - x start with 2, make it smaller
a number decreased by two x - 2 start with a number, make it smaller
two less than a number x - 2 start with a number, make it smaller
four more than a number x + 4 or 4 + x start with a number, add 4
the difference between 6 and a number 6 - x subtract, starting with 6
subtract four from a number x - 4 starting with a number, subtract 4
the sum of 4 and a number x + 4 or 4 + x add to get a sum
the opposite of the sum of a number and three -(x+3) or -(3+x) take sum, take opposite of sum
It may be convenient for the reader to use the technique the author used in writing the reason column.
Think of the word expression as a task to be completed by a computation.
Determine the operations needed.
Think how one would start and, then
think of what would need to be done to complete the task described.
Notice the uses of the preposition "of" in the last example. Prepositional phrases break up the expressions into pieces. Those beginning with "of" are discussed on the last page.
Below, notice how the prepositional phrases, in blue, which begin with by, between, from, and than, make it easier to examine the phrase and determine where to start and what to do.
wordsalgebraic symbolsreason
two decreased by a number 2 - x start with 2, make it smaller
a number decreased by two x - 2 start with a number, make it smaller
two less than a number x - 2 start with a number, make it smaller
four more than a number x + 4 or 4 + x start with a number, add 4
the difference between 6 and a number 6 - x subtract, starting with 6
subtract four from a number x - 4 starting with a number, subtract 4
the sum of 4 and a number x + 4 or 4 + x add to get a sum
the opposite of the sum of a number and three -(x+3) or -(3+x) take sum, take opposite of sum
Additional information is found in a prepositional phrases. The preposition "from" is almost always a tip-off that subtraction is required. Often, the desired mathematical expression starts with what is in the "from" prepositional phrase.
Multiplication & Division
Here are words associated with multiplication or division. The context is the key to the symbols needed, not the word itself. Remember, the word AND is a signal that there are two or more ideas, not that addition is required. Remember, to use prepositional and other phrases to break up the expression in order to determine what is required. Examples follow the list.
divide
quotient
halve, half
third
product
double
triple
square
wordsalgebraic symbolsreason
the product of two and a number 2x or 2(x) multiply
a third of the sum of a number and two (x + 2)/3 start with the sum, take a third of it
double the difference between 6 and a number 2(6-x) start with the difference, multiply by 2
triple the sum of four, five, and a number 3(4 + 5 + x) start with the sum, multiply by 3
the value of 4 nickels 4(5) or 5+5+5+5, etc. four fives or five four times
the value of some nickels 5x multiply 5 times a number
The last example may be HARD. Use the table below to examine the reason more clearly. The value of x nickels is 5x. The value of some nickels is 5x.
number of nickelsvalue of nickels
1 5(1) = 5
2 5(2) = 10
3 5(3) = 15
4 5(4) = 20
x 5(x) = 5x
Exercises
I. Write the expression/equation then check the answer.
Note: Your browser may print the answers with spaces that are not ment to be there.
1.) the square of five
Answers
5²
2.) the square of five subtracted from a number
Answers
x - 5²
3.) the opposite of a number
Answers
-x
4.) six less than half of a number
Answers
x/2 - 6 or .5x - 6
5.) the product of a number and four
Answers
4(x) or 4x or (4)(x)
6.) a number decreased by five
Answers
x - 5
7.) five less than a number
Answers
x - 5
8.) Ten is five less than a number.
Answers
10 = x - 5
9.) A number is less than five.
Answers
x < 5
See additional info on these.
10.) one less than a number
Answers
x - 1
11.) one less than a double a number
Answers
2x - 1
12.) the opposite of the sum of a number and 12
Answers
-(x + 12)
13.) triple a number
Answers
3x
14.) twice the sum of a number and 1
Answers
2(x + 1)
III. Complete the table. Check each answer.
wordsalgebraic symbols
1.
Answers
one less than a number
x - 1
2. the sum of six and double a number
Answers
6 + 2x or 2x + 6
3. double the sum of six and a number
Answers
2(x + 6)
4. the sum of three consecutive integers
Answers
first + second + third
(x) + (x + 1) + (x + 2)
5. the product of 2 consecutive odd integers
Answers
(first)(second)
(x)(x + 2)
IV. Complete the table. Check each answer.
wordsalgebraic symbols
1. one more than a number
Answers
x + 1 or 1 + x
2.
Answers
one less than a number or a number decreased by one
x - 1
3. the product of a number and 3 and a different number
Answers
3xy
4.
Answers
double a number or the product of a number and two
2x
5.
Answers
the square of a number or a number multiplied by itself
x2
