VERBAL PHRASE TO TWO STEP EXPRESSIONS OR EQUATIONS

To translate words to algebraic equations or expressions, we should know about what are words to be used to represent algebraic operations.

For addition (+) :

Sum, plus, more than, added to,.........

For subtraction (-) :

Difference, less than, reduced, subtracted from ...................

For multiplication (x) :

Times, product, multiplied by,...........

For division (/) :

Divided by, quotient, ............

Translate the verbal phrase to algebraic expressions.

Problem 1 :

Six less than twice a number x is four

Solution :

Six less than = -6

Twice a number = 2x

is = equal sign


2x - 6 = 4

Problem 2 :

Four more than the product of 2 and a

Solution :

Four more than = + 4

Product of 2 and a = 2a


4 + 2a

Problem 3 :

Nine times a number decreased by four

Solution :

Let the number be x.

Nine time a number = 9x

Decreased by 4 = -4


9x - 4

Problem 4 :

Seven more than the quotient of a number and 2 is 10

Solution :

Let the number be x.

Seven more than = +7

Quotient of a number and 2 = x/2

is = equal sign


(x/2) + 7 = 10

Problem 5 :

One less than the product of four and a number is 11.

Solution :

Let x be the required number.

One less than = -1

Product of 4 and a number = 4x

is = equal sign


4x - 1 = 11

Problem 6 :

Ten more than the quotient of a number and 3 is 12.

Solution :

Let x be the required number.

Ten more than = +10

Quotient of a number and 3 = x/3

is = equal sign


(x/3) + 10 = 12

Problem 7 :

 The sum of 9 and the quotient of x and 7 is 11.

Solution :

Sum of 9 = +9

Quotient of x and 7 = x/7

is = equal sign


(x/7) + 9 = 11

Problem 8 :

The product of 8 and the difference of n and 3.

Solution :

Product of 8 = 8

Difference of n and 3 = n - 3


8(n - 3)

Problem 9 :

1) Two less than the quotient of 15 and a number.

(15/x) - 2

2)  Five times the sum of six and some number.

Let x be some number.

5(x + 6)

3) The quotient of 7 and d decreased by 9.

d decreased by 9 :

d - 9

7/(d - 9)

4) Twice the difference of y and three

2(y - 3)

5) The difference of 9 and the quotient of s and –4

9 - s/(-4)

9 + (s/4)

6) The sum of 5 and product of 7 and x

5 + 7x

7) Three more than quotient of 5 and a 

3 + (5/a)

8) The product of 4 and the difference of x and 3

4(x - 3)

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