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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

2. Use the numbers 20, 40, and 80 to make a pattern whose sum lies between 1600 and 2000.
3. Take the numbers 12, 19 and 23. Obtain the result 4 – 2 – 1 based on Collatz conjecture. Which of
the three numbers takes the minimum steps and maximum steps to satisfy the conjecture?
4. Try to reach the Kaprekar constant starting from the following numbers. How many rounds do
they take to reach the constant?
(a) 1738 (b) 2964 (c) 3214 (d) 4075
5. Take the number 346 and make a Kaprekar constant of 3 digits. How many steps do you take to reach
the constant?
6. There are 3 matchstick patterns. Count the number of matchsticks used.

Can you see a pattern in it? Fill the box according to the pattern you observe.

Pattern Number 1 2 3 4 5 ---- 10
Number of Matchsticks
7. Write down a 4-digit palindromic number. Now, do the process to reach the Kaprekar constant. (All
digits should not be same.)

Breaking up Numbers

We are aware of the expanded form of a number. Recall that when a number is expressed as the
sum of place value of each digit, it is called the expanded form of that number. For example, the
expanded form of 81937 is
81937 = 80000 + 1000 + 900 + 30 + 7
= (8 × 10000) + (1 × 1000) + (9 × 100) + (3 × 10) + (7 × 1)
In this class, we will learn to express a number as the sum and difference of two or more numbers.
Adding and Subtracting

Sunidhi’s mother bought a saree for `2950. Mother asked Sunidhi to pay the amount in cash.

91 Number Play