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.

The difference of p to the fourth power and 9

9 less than p to the fourth power

The sum of 7 times m cubed and x times y

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