# Variables and Expressions

The basic concept of variables and expressions are discussed while solving the questions on algebraic expressions.

A variable is an alphabet that represents the value that can be change.

A constant is a value which will remain same.

A numerical expression contains only numeric constants and operations like addition (+), subtraction (–), multiplication (×) and division (÷).

An algebraic expression contains both numeric and variables constants and also operations like addition (+), subtraction (–), multiplication (×) and division (÷).

Algebraic expressions can be formed using variables, These expressions with variables are obtained using the operations; addition, subtraction, multiplication or division.

How to evaluate an expression?

To evaluate an expression is to find its value of the expression.

In solving the questions on variables and expressions some of the key words and phrases play an important role to translate between algebraic expressions and words. To evaluate algebraic expressions we need substitute the given values for the variables and simplify to find the value of the expression.

Addition (+) is also known as plus, sum, increased by, put together, combined

Subtraction (–) is also known as minus, difference, less than, find how much more or less

Multiplication (×) is also known as times, product, equal groups of, put together equal groups

Division (÷) is also known as divided by, quotient, separate into equal groups

Let us discuss how algebraic expressions are formed:

### I. Algebraic Expressions Formed Using Addition:

 Expressions(i) y + 8(ii) y + x(iii) 3p + (- 4q) Meaning8 is added to y.x is added to y.Sum of 3p and - 4q

### II. Algebraic Expressions Formed Using Subtraction:

 Expressions(i) x - 5(ii) a - b(iii) b - a Meaning5 is subtracted from x.The difference between a and b, when a > b .The difference between b and a, when a < b.

### III. Algebraic Expressions Formed Using Multiplication:

 Expressions(i) 15x(ii) 7a(iii) pq Meaningx is multiplied by 157 times aProduct of p and q.

### IV. Algebraic Expressions Formed Using Division:

 Expressions(i) $$\frac{x}{7}$$(ii) $$\frac{15}{a}$$(iii) $$\frac{y}{5}$$ Meaningx is divisible by 715 is divisible by ay is divisible by 5

## Solved Examples on Expressions Using Variables:

1. Write two ways of each algebraic expression in words.

(a) m + 7

Solution:

(i) the sum of m and 7

(ii) m increased by 7

(b) z - 11

Solution:

(i) 11 less than z

(ii) the difference of z and 11

(c) 5 × a

Solution:

(i) 5 times a

(ii) the product of 5 and a

(d) b ÷ 9

Solution:

(i) b divided by 9

(ii) the quotient of b and 9

2. Write an algebraic expression for each verbal expression.

(a) a number m minus five

Solution:

The word ‘minus’ implies subtraction.

Let m represent the number.

Thus, the algebraic expression is m - 5.

(b) the sum of two times a number k and seven

Solution:

The word ‘times’ implies multiplication.

Therefore, the expression can be written as 2k + 7

(c) two third of a number x plus ten

Solution:

The word ‘of implies multiplication.

Therefore, the expression can be written as (2/3) x + 10

(d) the product of 7 and m to the fifth power.

Solution:

The word ‘product implies multiplication.

The word ‘power implies exponent.

Therefore, the expression can be written as 7m5

3. Write a verbal expression for each algebraic expression.

(a) p4 - 9

Solution:

The difference of p to the fourth power and 9

Or

9 less than p to the fourth power

(b) 7m3 + xy

Solution:

The sum of 7 times m cubed and x times y

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