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:
Expressions (i) y + 8 (ii) y + x (iii) 3p + (- 4q) |
Meaning 8 is added to y. x is added to y. Sum of 3p and - 4q |
Expressions (i) x - 5 (ii) a - b (iii) b - a |
Meaning 5 is subtracted from x. The difference between a and b, when a > b . The difference between b and a, when a < b. |
Expressions (i) 15x (ii) 7a (iii) pq |
Meaning x is multiplied by 15 7 times a Product of p and q. |
Expressions (i) \(\frac{x}{7}\) (ii) \(\frac{15}{a}\) (iii) \(\frac{y}{5}\) |
Meaning x is divisible by 7 15 is divisible by a y is divisible by 5 |
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}From Variables and Expressions to HOME PAGE
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