6th Maths Term 1 Chapter 2 Exercise 2.3 Introduction to Algebra Solutions

6th Maths : Term 1 Unit 2 : Introduction To Algebra

Exercise 2.3 - Miscellaneous Practice Problems

1. Complete the following pattern.

9 – 1 =

98 – 21 =

987 – 32 =

9876 − 432 =

98765 − 54321 =

What comes next?

9 – 1 = 8

98 − 21 = 77

987 − 321 = 666

9876 − 4321 = 5555

98765 − 54321 = 44444

987654 − 654321 = 3333333

2. A piece of wire is ‘12s’ cm long. What will be the length of the side, if it is formed as
(i) an equilateral triangle
(ii) a square?

(i) equilateral triangle = 3 equal sides

A piece wire [circumference] = 12s

one side length = 12s / 3

= 4s

(ii) Square = 4 equal sides

Circumference = 12s

One side length = 12s / 4

= 3s

3. Identify the value of the shapes and figures in the table given below and verify their addition horizontally and vertically.
Grid Puzzle
Shape values
Horizontal/Vertical Verification
4. The table given below shows the results of the matches played by 8 teams in a Kabaddi championship tournament.
Kabaddi tournament table

Find the value of all the variables in the table given above.

k = 8 – 5 = 3

a = 7 + 2 = 9

x = 8 – 4 = 4

m = 7 – 6 = 1

b = 9 – 3 = 6

y = 6 + 3 = 9

n = 4 + 6 = 10

c = 10 – 6 = 4

Final values: k = 3; m = 1; n = 10; a = 9; b = 6; c = 4; x = 4; y = 9.

Challenging Problems

5. Gopal is 8 years younger to Karnan. If the sum of their ages is 30, how old is Karnan?

Age of Karnan = x

Age of Gopal = y

Gopal is 8 years younger to Karnan

i.e., y = x − 8

sum of their age = 30

x + y = 30

x + (x − 8) = 30

x + x − 8 = 30

2x − 8 = 30

2x = 30 + 8

2x = 38

x = 38 / 2 = 19

Age of Karnan is ‘19’ years.

6. The rectangles made of identical square blocks with varying lengths but having only two square blocks as width are given below.
Rectangles P Q R S

(i) How many small size squares are there in each of the rectangles P, Q, R and S?

P = 2, Q = 8, R = 6, S = 10

(ii) Fill in the boxes.

Box filling question
Filled boxes solution
7. Find the variables from the clues given below and solve the cross-word puzzle.
Empty Crossword

Across

  • x + 40 gives 100
  • 7 reduced from t gives 31
  • z is 5 added 5 times
  • v is the whole number zero plus number of days in a year
  • k is 24 added to 25
  • u is 2 added to two times 11 gives the number of hours in a day
  • a is 20 more to 40
  • s minus 1 gives 246 is the number of letters in Tamil language

Down

  • x is 1005 multiplied by 6
  • t ÷ 7 = 5
  • p is the predecessor of first 3 digit number
  • z is the number of weeks in a year (digits reversed)
  • k is 11 times 4
  • u is product of 23 and 9
  • a is 4 added to the product of 12 and 5
  • m is the successor of 9
Solved Crossword