Page 80 - Ganit Kaushal

10. Write all three-digit palindromes using the digits 4, 0, and 5.

11. Do you remember any English words that are palindromes? Write as many such words as you can.
12. If the time now is 12:21 p.m., this is a palindromic time. After how much time will you get the next
palindromic time, and what will it be? What about the one after it?
13. How many different calendars do we have that serve for all the years from the past and the future?

3.12 MENTAL MATH

We have already learnt addition, subtraction and multiplication of natural 25,000
numbers with the help of a number line. Here we will learn addition, 38,400 200 3,200
subtraction, and multiplication of numbers mentally using boxes and arrows 28,000 13,000 63,000
in a more playful manner. 61,600 1,500 19,500
31,000 20,900
Have a look at the adjoining figure. 60,000
What can you say about the numbers and the lines drawn?
In fact, the picture explains the procedure of addition in a more interesting and playful manner. The
numbers in the middle column are added in different ways to get the numbers on the sides (1500 +
1500 + 200 = 3200). The numbers in the middle can be used as many times as needed to get the desired
sum. Draw arrows from the middle to the numbers on the sides to obtain the desired sums.
Two examples are given. It is simpler to do it mentally!

(a) 38,400 = 25,000 + 200 × 2 + 13,000 (Shown with the help of the arrows on the left-hand side,
200 is multiplied by two, because two arrows are coming out of the box containing 200)
(b) 3200 = 1500 × 2 + 200 (Shown with the help of arrows on the right-hand side)
Can we make 900 using the numbers in the middle?
The answer is no, because only addition is allowed. All the numbers except 200 are greater than 900,
and no multiple of 200 gives 900.
What about 14,000, 15,000, and 16,000?
Readers are advised to find the answer to these questions.

Adding and Subtracting
Now, we are allowed to use both addition and subtraction of the numbers in the boxes (see 40,000 7,000
picture) to get the required number. It will be a fun-filled mental game to use the addition 300 1,500
and subtraction of numbers in the boxes to achieve a given number. 12,000 800
For example:

(a) 38,800 = 40,000 – 4 × 300 or 5 × 7,000 + 2 × 1,500 + 800
(b) 45,000 = 40,000 + 12,000 – 7,000
® Readers are advised to explore if there are many more ways to get these numbers.

Digits and Operations
Can you give an example of two 5-digit numbers such that their addition also gives a 5-digit number?
The answer is yes. Here it is: 12,250 + 23,535 = 35,785.

Can you give an example of subtracting two 5-digit numbers to get another 5-digit number?
The answer is yes. Here, it is 47,842 – 22,544 = 25,298.

78 Mathematics-6