Algebra For Class 6

If we wish to define what is algebra, we can say it as a branch of mathematics in which we use letters to denote numbers. Now these letters are nothing but the english alphabets that we have studied and known so far. In algebra, we assume the value of some unknown numerical constant to be a variable in an equation and then we solve the equation till we find the unknown quantity.

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This Story also Contains

1. What is Algebra?
2. Algebra Class 6 Notes
3. Algebra Class 6 Questions and Answers

This article is about the concept of algebra class 6 ncert. In this article, we will learn about introduction to algebra class 6, the basics of algebra, algebra class 6 solutions, etc.

What is Algebra?

Algebra is a branch of mathematics that deals with variables and constants. An algebraic expression is a combination of variables and constant. Algebra includes almost everything ranging from solving elementary equations to the study of abstractions. It is really helpful in finding the unknown quantities assuming them as variables and solving the equations.

We use letters called variables, to represent the unknown quantities in maths. The use of letters helps us in various ways as listed below:

• It makes the process of writing rules and formulas in very simple way.
• We do not have to talk about just one number but we can talk of many numbers at the same time.
• The variables help us to represent unknown quantities and solve daily life problems within no time.
• They also enable us to perform mathematical operations like addition, subtraction, multiplication, and division on numbers in form of variables.

Algebra Class 6 Notes

Algebra class 6 notes include the concepts of variables and constants, algebraic equations and how to solve such equations.

Variable and Constants

A variable is a quantity that may change. Hence, its value is not fixed and may take different values. Variables are expressed as small letters like a,b,c,x,y,z,....

A constant is a quantity that does not change.

For example, you and your friend go to buy pencils. The cost of one pencil is Rs. 5. The amount to be paid is $5x$ where $x$ is the number of pencils. You buy 5 pencils and your friend buys 4 pencils. Here, the value of $x$ is 5 and 4. From this, we could say that the value of $x$ is not fixed, it keeps on changing. So, $x$ is a variable.

But the price of the pencil is not going to change. So, the cost of one pencil that is Rs.5 is a constant.

Similarly, consider the area of square formula, $A = x^2$. Here, the length of the side$(x)$ is not fixed. So, $x$ is a variable. But the number sides in a square is always four. So, 4 is a constant.

Algebraic Equations

Algebraic equations are combinations of variables and constant. Eg. $2x=38$, $3x+7y=22$, etc.

Algebraic equations with one variable

Let us consider the previous example. You go to buy pencils. The cost of one pencil is Rs. 5. You pay Rs.35 to the shopkeeper. Let $x$ be the number of pencils.

Now, let us form a algebraic equation for this situation. The algebraic equation is $5x = 35$ where $x$ is the number of pencils.

By solving this equation, we can find the number of pencils you bought.

Now, let us look into another example to understand the algebraic equation with two variables.

Algebraic equations with two variables

Raju and Balu are brothers. When Raju is 12 years old, Balu is 9 years old. When Raju is 15 years old, Balu is 12 years old. From this, we could say that Raju is 3 years older than Balu.

Now let $y$ be Raju's age and $x$ be Balu's age. This can be expressed as a algebraic equation as $y = x+3$. If we know Balu's age, then, we can put the value in $x$ and find Raju's age. Suppose Balu is 20 years old, then Raju's age is, $y=20+3 = 23$.

Similarly, if we know Raju's age, then, we can put the value in $y$ and find Balu's age. Suppose Raju is 17 years old, then Balu's age is, $17 = x+3$. This can be written as $x=17-3 = 14$. So, Balu is 14 years old when Raju is 17 years old.

How do we solve an algebraic equation?

We solve equations until the left hand side equation is equal to right hand side equaiton. For example, equation 2x = 4 is satisfied for the value of x = 2 only. As we can write $x = \frac{4}{2} = 2$.

Now, let us look into some algebra class 6 extra questions.

Algebra Class 6 Questions and Answers

Example 1: Cadets are marching in a Republic Day parade. There are 10 cadets in a row. Find out the rule which gives the number of cadets.

Solution: Let us suppose that $p$ be the number of rows
Given that number of cadets present in a row $=10$
Hence total number of cadets $=$ number of cadets in a row $\times$ total number of rows $
=10 p
$

Example 2: If there are $\mathbf{2 0}$ pencils in a box, how will you write the total number of pencils in terms of the number of boxes?

Solution: Let us suppose that $x$ be the number of boxes
Given that number of pencils in a box $=20$
Hence total number of pencils $=$ number of pencils in a box $\times$ total number of boxes $=20 x$

Example 3: The professor in a college distributes 2 fountain pens per student. Can you tell how many pens are needed in all ?

Solution: Let us take $r$ be the total number of students
From question, pens given to each student $=2$
Therefore total number of pens $=$ number of pens given to each student $\times$ total number of students $=2 \mathrm{r}$

Example 4: An eagle flies 3 km in one minute. Express the distance covered by the eagle in terms of its flying time in minutes.

Solution: Let z minutes be the flying time
We are given that distance covered in one minute $=3 \mathrm{~km}$
Hence, distance covered in z minutes $=$ Distance covered in one minute $\times$ total flying time $=1 \times z=z \mathrm{~km}$

Example 5: The side of a square is denoted by p. Express the perimeter of the square using
p.

Solution: Side of square $=p$
Perimeter of square $=p+p+p+p=4 p$

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