Algebra worksheet for class 6

 

Class 6 Algebra Worksheet

Part A: Understanding Variables and Expressions

1. Fill in the blanks:
   a. In algebra, letters like $x, y,$and $z$ are called __________.
   b. An algebraic expression combines numbers, variables, and __________ (e.g., $+, -, \times, \div$).

2. Identify the variable(s) in each expression:
   a. $5x + 3$
   b. $2y - 7$
   c. $3a + 2b - 4$
   

3. Write an algebraic expression for the following:
   a. A number increased by 5.
   b. Three times a number minus 2.
   c. The sum of a number and 12, divided by 4.

Part B: Simplifying Expressions

4. Simplify the following expressions:
   a. $2x + 3x$
   b. $4y - 2y + 7$
   c. $5a + 3 + 2a - 1$
   

5. Combine like terms:
   a. $6m + 2n + 4m$
   b. $10p - 3p + 8$
   c. $x + x + x + 5$
   

Part C: Solving Equations

6. Solve for $x$ :
   a. $x + 5 = 12$
   b. $3x = 15$
   c. $2x + 4 = 10$
   

7. If $a = 3$, 
   $b = 2$ and $c = 5$ evaluate the following:
   a. $a + b$
   b. $2c - a$
   c. $b^2 + c$
   

Part D: Word Problems

8. Translate the following into algebraic expressions:
   a. The age of John is 5 years more than twice his brother’s age. If his brother’s age is $x$ what is John’s age?
   b. A rectangle’s length is $3$ times its width. If the width is $w$ write an expression for the length.

9. Solve the problem:
   a. A book costs $x$ rupees. If you buy 4 books and spend 200 rupees, find the cost of one book.
   b. A car travels $60$ kilometers per hour. Write an expression for the distance traveled in $t$ hours.

Bonus Questions

10. If $2x - 3 = 7$ find the value of $x$.
11. A fruit seller sells apples and bananas. He sells $3x$ apples and $2x$ bananas. If the total number of fruits sold is 50, how many apples and bananas did he sell?