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Intro

Two Numbers -- One Operation: Addition & Subtraction

This passage presents words related to each of the basic operations. the reader should already be familiar with these words but, links have been provided in case a review is desired.

Here are words associated with addition or subtraction. The context is the key to the symbols needed, not the word itself. Examples follow the list.

 words algebraic symbols reason 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.

1. Think of the word expression as a task to be completed by a computation.
2. Determine the operations needed.
3. Think how one would start and, then
4. 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.

 words algebraic symbols reason 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.

 words algebraic symbols reason 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 nickels value 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
2.) the square of five subtracted from a number
3.) the opposite of a number
4.) six less than half of a number
5.) the product of a number and four
6.) a number decreased by five
7.) five less than a number
8.) Ten is five less than a number.
9.) A number is less than five.
10.) one less than a number
11.) one less than a double a number
12.) the opposite of the sum of a number and 12
13.) triple a number
14.) twice the sum of a number and 1

III. Complete the table. Check each answer.
 words algebraic 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.
 words algebraic 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                    © 01-8-23 www.mathnstuff.com/math/algebra/qb/awrite2.htm