Each of our Ganita Prakash Class 8 Worksheet and NCERT Class 8 Maths Chapter 6 Algebra Play Worksheet with Answers focuses on conceptual clarity.
Algebra Play Worksheet Class 8
Class 8 Maths Algebra Play Worksheet
Algebra Play Class 8 Ganita Prakash Worksheet
Thinking about ‘think of a number’ tricks
Riya tells Aman a maths trick.
“Think of any number. Double It, add 4, divide by 2, now subtract the number you first thought of.” Aman follows the steps and is surprised by the final answer.
Question 1.
If Aman things of the number 9 and follows the given steps, verify whether the final result is 2.
Question 2.
Choose the number 6 and perform the steps. Write the result after each step.
Question 3.
Does the final answer change when the starting number changes?
Answer:
No
Question 4.
Why do you think this trick always works?
Answer:
Question 5.
Write each step of the trick using algebraic expressions.
Question 6.
If Amari wants the final answer to be 6 instead of 2. Which step of the original trick would you change?
Answer:
Add 12 instead of 4.
Question 7.
Write new steps so that the final answer becomes 6.
Shabnam thinks of a special date and follows a set of steps instructed by Sohil. Sohil correctly guesses the date without being told directly.
Let us see, how?
Sohil asks Shabnam to follow the given steps:
Let the month be M and the day be D.
- Multiply M by 5 : 5M
- Add 6 = 5M + 6
- Multiply by 4 : 20M + 24
- Add 9 : 20M + 33
- Multiply by 5 : 100M + 165
- Add the day = 100M + 165 + D, after the process Shabnam’s answer is 394.
Now, Sohil subtracts the magic number 165 from 394 (394 – 165 = 229)
And says, “You are thinking of 29th February.”
Question 8.
If the final answer is 673, find the date Sohil finds.
Answer:
8th May
Question 9.
If Sohil thinks of his birthday, explain the mathematical steps used to determine Sohil’s birthday from the result of 467.
Answer:
2nd March
Number Pyramids
In a number pyramid, each block is the sum of the two blocks directly below it.
Question 10.
Fill in the missing numbers in the given number pyramids.
Answer:
Question 11.
Draw your own. number pyramid and fill them,
Answer:
Question 12.
Fill the following number pyramids.
Answer:
Question 13.
Find the value of letter-numbers in the following pyramids.
Answer:
(a) a = 5, b = 17, c = 28, d = 44, e = 58, f = 102
(b) p = 19, q = 4, r = 34, s = 61, t = 53, u = 114
Question 14.
For a number pyramid with bottom row as a, b and c write an expression for the top row of the pyramid. If a = 2, b = 5 and c = 7, find the top number without drawing the pyramid.
Answer:
a + 2b + c, 19
Fun with Grids
Calendar Magic
Question 15.
Raghav created a trick using a calendar, where he choose a 2 x 2 grid from August 2025. The sum of all four numbers in the grid was 48. If the sum of the numbers in the grid is represented, algebraically how can Raghav find the individual numbers? Explain.
Answer:
| 8 | 9 |
| 15 | 16 |
Question 16.
Use a L-shaped grid from the given calendar. Write the expressions for all numbers. Find the total sum algebraically.
Answer:
Algebra Grid
Question 17.
In the following grid, shapes represent numbers. Each row and column ends with the sum of the values of the shapes in that row or column.
Find the values of the shape and fill in the empty squares:
Answer:
The Largest Product
Question 18.
Maya and her friend Aarav wanted to find the largest product using the digits 2, 3, and 5. After exploring six possible arrangements, Maya correctly deduced that the largest product is 32 × 5. Explain how she arrived at this conclusion.
Answer:
Question 19.
Fill the digits 4, 5, and 9 in. 
to make the largest product possible.
Answer:
54 × 9
Question 20.
Explain why placing the largest digit as the multiplier works best. Write a general rule in your own words.
Answer:
Decoding Divisibility Tricks
Question 21.
Ayesha used a divisibility trick with a two-digit number. She reversed the digits, found the difference between the original number and the reversed number, and divided result by 9. She always obtained no remainder. How does algebra kelp explain this trick?
Answer:
Question 22.
Check whether the sum of all three numbers formed by interchanging the digits of the number 117 is divisible by 111.
Answer:
Yes.
Question 23.
Check whether the sum of all the numbers formed by the digits of the number 235 is divisible by 222 and 37.
Answer:
Yes
Question 24.
The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number formed is 27 less than the original number. Find the number.
Answer:
63
Question 25.
Consider any three-digit number, say abc (100a + 10b + c). Create two new three-digit numbers by cycling the digits around, forming bca and cab. Now add the three numbers. Using algebra, prove that the sum is always divisible by 37. Will the sum always be divisible by 3 as well? Why or why not?
Answer:
Yes
Question 26.
Two friends, Meera and Shanti, are dairy farmers. One day, they meet each other with their cows. Meera says, “You have 3 times as many cows as I do.” Shanti replies, “That’s true, but if I gave you 5 of my cows, we would have the same number of cows.” How many cows do Meera and Shanti have?
Answer:
Meere : 5 cows, Shant : 15 cows
Question 27.
A father Is 3 times his son’s age. In 12 years, the father will be twice his son’s age. How old is the son now?
Answer:
12 Years
Question 28.
Ravi runs a small sandwich stall, and his expenses are as follows:
. Rent for the stall: ₹4000 per day
. The cost of making one sandwich (including all the ingredients and utilities): ₹20
(a) If Ravi can sell 100 sandwiches a day, what should be the selling price of each sandwich to make a profit of ₹2000?
Answer:
₹ 80
(b) If Ravi’s customers are willing to pay only ₹ 50 for a sandwich, how many sandwiches should he aim to ‘self in a day to make a profit of ₹ 2000?
Answer:
₹ 200
Question 29.
Karim saw a dream, in the dream, a genie gave Karim a challenge. Karim decided to try the genie’s challenge. He started with a certain number of coins, and each time he went around the tree, the number of coins doubled, but he had to give 8 coins to the genie each time. After three rounds, he was left with only 8 coins. How many coins did Karim initially have?
Answer:
8 conins
Question 30.
Maya found a wishing well that doubles any coins thrown into it, but the well collects a fee of 12 coins after every doubling. Maya threw in her coins, and after two rounds, she was left with exactly 20 coins. How many coins did Maya have at the start?
Answer:
14
Worksheet On Algebra Play Class 8
A. Choose the correct option.
1. What Is the final result of the ‘Think of a Number’ trick when doubling a number, adding 10, dividing by 2, and subtracting the original number?
(a) 4
(b) 5
(c) 2
(d) 1
Answer:
(a) 4
2. In a number pyramid, if the base has numbers 3, 4, and 9 what is the number at the top?
(a) 20
(b) 11
(c) 24
(d) 16
Answer:
(a) 20
3. In the Calendar Magic trick, if the sum of the four numbers in the 2 x 2 grid is 44, what will be the value of a, where a is the top left number?
(a) 7
(b) 6
(c) 5
(d) 8
Answer:
(a) 7
4. In the trick involving reversing two-digit numbers and subtracting them, the difference will always be divisible by:
(a) 4
(b) 5
(c) 9
(d) 11
Answer:
(c) 9
5. Using the digits 6, 3, and 5 only once to form a product, which arrangement gives the largest product?
(a) 65 × 3
(b) 53 × 6
(c) 36 × 5
(d) 56 × 3
Answer:
(b) 53 × 6
Question 6.
In the Think of a Date’ trick, your friend tells you their final result is 1269, what is the date they thought of?
(a) 2nd October
(b) 4th November
(c) 9th December
(d) 26th January
Answer:
(b) 4th November
7. In a 3-row number pyramid where the bottom row has the values a, b, and c, what is the simplified algebraic expression for the single number at the very top?
(a) a + b + c
(b) 2a + 2b + 2c
(c) a + 2b + c
(d) a2 + b2 + c2
Answer:
(c) a + 2b + c
8. If the first three Virahanka numbers are placed in the bottom row of a 3-row number pyramid, what number will be at the very top?
(a) 6
(b) 8
(c) 10
(d) 7
Answer:
(b) 8
Directions. (For Q.9 – 10): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
9. Assertion (A): In a number pyramid with four rows and bottom row values a, b, c, and d, the top-most number is a + 3b + 3c + d.
Reason (R): Each number in a number pyramid is the sum of the two numbers directly below it.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
10. Assertion (A): A 6-digit number formed by repeating a 3-digit number (like 123123) is always divisible by 1001.
Reason (R): The number 1001 is the product of the prime numbers 7, 11, and 13.
Answer:
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
B. Fill in the blanks.
1. In a 3 × 3 grid on a calendar, if the middle number is n, the sum of all nine numbers in the grid can be represented algebraically as ______ .
Answer:
9n
2. The sum of any two-digit number and its reverse two-digit number is always divisible by ______.
Answer:
11
3. A two-digit number 10 a + b minus its reverse 10 b + a is always a multiple of ______.
Answer:
9
4. To maximise the product (two-digit number) × (one-digit number), using three different non-zero given digits, the ______ digit should be used as the one-digit multiplier.
Answer:
largest
5. In the ‘Think of a Date’, trick the final result given to the friend is 100M + D + 165. To find the birth month M and day D, you must subtract ______ from the final result.
Answer:
165
C. State whether the following statements are true (T) or false (F).
1. In the Think of a Number’ trick, the end result is always 2 regardless of the starting number choosen.
Answer:
54, 62
2. In a number pyramid, each number is the product of the two numbers directly below it.
Answer:
1, 2, 3, 5; 3, 5,8; 8,13, 21 yes
3. In the date trick, if the final answer is 1390, the date thought of was the 25th of December.
Answer:
| 13 | 14 |
| 20 | 21 |
4. If the bottom row of a 4-row pyramid contains the first four Virahanka-Fibonacci numbers (1, 2, 3, 5), the number at the top is 18.
Answer:
(a) 49
(b) 110
5. To form the largest product of (two-digit) × (one-digit), the smallest digit should be used as the multiplier.
Answer:
D. Solve the following.
Question 1.
The difference between two numbers is 8. If the larger number is subtracted from three times the smaller number, the difference is 100. Find the numbers.
Answer:
Question 2.
If the bottom row of a 4-row pyramid contains the first four Virahanka-Fibonacci numbers (1, 2, 3, 5), calculate all the values in the pyramid. Discuss whether the numbers generated in the higher rows are also Virahanka numbers.
Answer:
Question 3.
Prove that for any 2 × 2 grid on a calendar, the sum of the four numbers is always 4a + 16, where a is the top-left number. Use this to find the numbers in a grid where the sum is 68.
Answer:
Question 4.
Find the number in the topmost row based on the given numbers in the bottom row, without constructing the entire pyramid in each case.
(a)
| 4 | 5 | 7 | 9 |
(b)
| 7 | 8 | 10 | 2 | 3 |
Answer:
Question 5.
A farm has horses (4 legs) and hens (2 legs) totalling 55 heads and 150 legs. Explain how to solve this problem using both algebraic equations and the logical method (without using letter-numbers).
Answer: