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 ‘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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