TRANSLATING VERBAL PHRASES TO ALGEBRAIC EXPRESSIONS

To translate words into an algebraic expression or equation, write the numbers and operations in the order they appear (working from left to right)

Problem 1:

5 more than 6 times a number

Solution :

Let the number be x.

6 times a number = 6x

5 more than 6 times a number = 6x + 5

Problem 2 :

8 less than a number, divided by 3

Solution :

Let the number be x.

A number divided by 3 = x/3

8 less than a number, divided by 3 = x/3 - 8

Problem 3 :

8 times the cube of a number

Solution :

Let the number be x.

8 times the cube of a number = 8x³

Problem 4 :

The sum of the square of a number and 4

Solution :

Let the number be x.

The sum of the square of a number and 4 = x² + 4

Problem 5 :

10 times the sum of a number and 9

Solution :

Let the number be x.

The sum of a number and 9 = x + 9

10 times the sum of a number and 9 = 10(x + 9)

Problem 6 :

18 fewer than half of a number

Solution :

Let the number be x.

Half of a number = x/2

18 fewer than half of a number = (x/2) - 18

Problem 7 :

The quotient of 8 and twice a number

Solution :

Let the number be x.

The quotient of 8 and twice a number = 8/2x

Problem 8 :

2 subtracted from the square of a number

Solution :

Let the number be x.

The square of a number = x²

2 subtracted from the square of a number = x² - 2

Problem 9 :

Twice the quantity of number decreased by seven

Solution :

Let the number be x.

Twice the quantity of number decreased by seven = 2x - 7

Problem 10 :

The sum of three times the quantity of a number increased by six and half the same number.

Solution :

Let the number be x.

= 3(x + 6) + (1/2)x

Problem 11 :

A quarter of the square of a number

Solution : 

Let the number be x.

A quarter of the square of a number = x²/4

Problem 12 :

12 divided by the difference of a number and 2

Solution :

Let the number be x.

The difference of a number and 2 = x - 2

12 divided by the difference of a number and 2 = (x - 2)/12

Problem 13 :

The sum of 4 times a number and that same number cubed.

Solution :

Let the number be x.

The sum of 4 times a number and that same number cubed = 4x + x³

Problem 14 :

The product of the quantity x plus y and the quantity x minus y

Solution :

Quantity x plus y = x + y

Quantity x minus y = x - y

The product of the quantity x plus y and the quantity x minus y

= (x + y) (x - y)