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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