"Variables and Expressions" is the basic topic required for the students who would like to study Algebra in math.
The Symbol which has no value is called as variable. The value of the variable may change from one problem to another problem.The alphabets are being used to represent variables.
Expression is an algebraic or mathematical statement involves numbers,one or more variables and the operation symbols like +,-, x ,รท.
To understand this topic better let us consider the following examples.
Example 1 x - 3 = 5 x = 5 + 3 x = 8 In this problem the value of the variable x is 8. |
Example 2: x + 1 = -3 x = -3 -1 x = -4 In this problem the value of the variable x is -4. |
In both the problem we are finding the value of the same variable "x". But we got different values. From this we come to know that the value of variable gets changed from one problem to another problem.
(i) 5x + 3
(ii) a - 9
(iii) 2y + 7
these are the examples of expressions.
An equation contains expressions that are separated by an equals sign.
2x - 4 is the example of expression.
2x - 4 = 5 is the example of equation.
The difference between them is just "equal sign".
Here you can find some basic ideas to write algebraic expressions from word problems. "Translating word problems into equations" is a much needed thing to the students who study math in all levels.
For some students, solving word problems in math is never being easy and always it is a challenging one. Once students understand the technique of solving word problems,it will become easy.
Let us take a example,
Cost of one chocolate is $2. From this we need to find the cost of 5 chocolates.
To find the cost of 5 chocolates we need to add 2 + 2 + 2 + 2 + 2 = 10. Instead of adding 2 five times simply we can multiply 5 and 2.So we will get 10.
Like that now we have to find the cost of "n" chocolates if the cost of one chocolate is $3. The answer is "3n".
Terms are being used in word problems |
Corresponding signs to be used |
more,sum difference,differ times (or) of is twice thrice |
+ (addition) - (Subtraction) x (Multiplication) = (equal to) Multiply by 2 Multiply by 3 |
Problem 1:
A taxi fare after each km when the fare is $15 for the first km and $8 for each km that he traveled. Find the total cost that he has to pay for the whole journey.
Solution:
Let "x" be the number of kilometer that he traveled additionally.
Total cost that he has to pay is 15 + 8x
Let us see the next example of "variables and expressions".
Problem 2:
John has 10 more marbles than Peter. Then find the total number of marbles.
Solution:
Number of marbles that Peter has = x
John is having 10 more marbles than Peter
The mathematical sign for the term more is "+" . 10 more means we have to write 10 + x.
Number of marbles that John has = 10 + x
Total number of marbles = x + (10 + x)
Let us see the next example of "variables and expressions".
Problem 3:
Write the algebraic expression for the product of two consecutive even integers.
Solution:
Let "x" be the even number
then "x+2" be the consecutive even number
the product of two consecutive even integer is x(x+2)
Let us see the next example of "variables and expressions".
Problem 4:
The length of the rectangle is twice its breadth. Write the algebraic expression to find its area.
Solution:
Let "x" be breadth of the rectangle
Length = twice its breadth
= 2x
Area of the rectangle = (Length + breadth)
= x x 2x
Let us see the next example of "variables and expressions".
Problem 5:
George made 54 chocolate cookies and some mango cookies.How many cookies did he make?
Solution:
Let "x" be number of mango cookies
Total number of cookies that he made is "54 + x"
Let us see the next example of "variables and expressions".
Problem 6:
Write the algebraic expression to show the sum of three consecutive numbers.
Solution:
Let "x" be number a number
Then "x + 1" and "x + 2" are the next two consecutive numbers
Sum of the numbers "x + (x + 1) + (x + 2)"
Problem 7:
"2 increased by a" write the algebraic expression for the above statement.
Solution:
"increased" means "positive" sign
"2 + a" is the algebraic expression for the above statement.