# 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 (÷).

**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

**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 ‘**sum**’ implies addition.

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.

The word ‘**plus**’ implies addition.

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 7m^{5}

**3. Write a verbal expression for each algebraic expression.**

**(a) ** p^{4} – 9

**Solution: **

The difference of p to the fourth power and 9

**Or**

9 less than p to the fourth power

** (b) ** 7m^{3} + xy

**Solution: **

The sum of 7 times m cubed and x times y