Addition and Subtraction of Algebraic Terms 

Addition in Algebra 

Let us understand this topic with an example. 

Mike has 20 more chocolate candies than Steve. Then exactly how many chocolate candies does Mike have? 

We shall denote Steve’s candies by the letter x. So “x” is a variable here. This can take any positive value. (because you can’t physically negative number of chocolate candies)  

Using x, we can write Mike’s chocolates as x+20.  

The expression (x+20) is read as “x plus 20”. Meaning 20 added to x.  

If x is 10, then Mike would have 10+20= 30 chocolates. 

However in this case, we do not know how many “exact” number of chocolates does Mike have, so we will say that the answer to above problem statement ends in a “variable” form. 

Example: 

Elma and Mona are sisters. Mona is younger than Elma by 4 years. When Mona =12 years, Elma is16 years. When Mona is 20 years, Elma is 24 years. We don’t know Mona’s age exactly. It may have any value. Let “x” denote Mona’s age in years. Then how would you represent Elma’s age in an expression? 

Answer 

Mona’s age = x years 

Elma is 4 years elders to Mona. 

So, Elma’s age= X + 4 

Subtraction in Algebra 

Let us consider another example to understand the concept of subtraction. 

Elma has made 10 donuts.  However, Elma has distributed some donuts among guests. Then how much is she left with? 

Let us denote the number of donuts distributed by Elma as x. “x” is a variable which can take different values.  

Number of donuts made by Elma is 10.  

So the number of Donuts Elma is left with can be represented by an expression (10 - x). The expression is represented as “10 minus x”.  

Example: 

Apples are to be filled from a large box to another but smaller box. When the small box is filled completely, the large box is left with 15 apples. Then how many apples does small box has? 

Solution 

Let initially, the number of apples in large box = X 

When small box is filled completely, the large box is left with 15 apples. Which means that we transferred “X-15” 

The number of apples in small box = X – 15 

Multiplication and Division 

We can multiply a constant and a variable or two variables to get a product. It also leads to algebraic expression. Similarly, we can divide two algebraic terms to get a quotient. It is also an algebraic term. To multiply or divide two algebraic terms, first we multiply or divide the constants, then the variables and finally we write the constant and variable together. 

Example: 

Evaluate:  4p × 2q 

Solution  

= 4 × p × 2 × q 

= (4 × 2) × (p × q) 

= 8 × pq 

= 8pq 

Here, 8 is the constant while p and q are the variables. 

Note: 30x and 30 + x are two different expression. In 30 x, x is multiplied by 30. In (30+x), 30 is added to x. 

Example: 

Students went to buy pencils from a stationary shop. The price of one pencil is $ 3. Gigi wants to buy few pencils. Then how much money should she carry? 

Solution 

Let us say, or assume, Gigi wants to buy “x” number of pencils. 

Since the price of each pencil is $ 3,  

Amount Gigi should carry = $ 3x 

Variable ‘x’ is multiplied by the unit price $3, (because 3 is constant)  

Example: 

4A ÷ 16 =?? 

Solution