Mental Math

Observe the figure below. What can you say about the numbers and the lines drawn?

Numbers in the middle column are added in different ways to get the numbers on the sides (1500 + 1500 + 400 = 3400).

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!

38,800 = 25,000 + 400 × 2 + 13,000

3400 = 1500 + 1500 + 400

Can we make 1,000 using the numbers in the middle? Why not? What about 14,000, 15,000 and 16,000?

YesNo, it is possible. Explore how. What thousands cannot be made?

Here, using the numbers in the boxes, we are allowed to use both addition and subtraction to get the required number.

An example is shown.

39,800 = 40,000 - 800 + 300 + 300

45,000 = + -

5,900 = - -

17,500 = + -

21,400 = + + + +

An example of adding two 5-digit numbers to get another 5-digit number is 12,350 + 24,545 = .

An example of subtracting two 5-digit numbers to get another 5-digit number is 48,952 - 24,547 = .

Figure it out 6

1. Write an example for each of the below scenarios whenever possible.

Could you find examples for all the cases? If not, think and discuss what could be the reason. Make other such questions and challenge your classmates.

(a) Let’s divide 90, 250 by 2

Then, 902 = + 2502=

Hence to get sum more than 90,250 both numbers should be moreless than 45,125

(b) To get a 6 digit sum by adding 5 digit and 3 digit, the 5 digit number should be more than 99,001.

(c) Let’s take minimum 4 digit number 1000.

let’s add them

which is a 4 digit number.

Hence 6 digit sum’ from 4 digit number is impossiblepossible.

(d) Let’s take 5 digit numbers 67987 and 65783

let’s add them

which is a digit number

(e) Let’s take minimum 5 digit numbers 1000

let’s add them

which is a 5 digit number.

Hence 6 digit sum from 5 digit numbers is impossiblepossible.

(f) 5-digit -5 digit to given below.

give a difference less than 56,503 <>= 56503

(g) 5-digit-3 digit = 1 008 6 (5 digit) to give a 4 digit = + 875 (3 digit) , difference = 92 11 (4 digit)

(h) 5-digit digit = 1 2 8 7 6 (5 digit) to give a 4 digit = -7865 (4 digit) , difference = 5 0 11 (4 digit)

(i) 5-digit -5 digit 7 = 645 3 (5 digit) to give a 3 digit = 76 145 (5 digit) difference = 308 (3 digit)

(j) 5-digit -5 digit

Not possiblepossible to give 91,500

2. Always, Sometimes, Never?

Below are some statements. Think, explore and find out if each of the statement is ‘Always true’, ‘Only sometimes true’ or ‘Never true’. Why do you think so? Write your reasoning and discuss this with the class.

a. 5-digit number + 5-digit number gives a 5-digit number: SometimesNeverAlways true

b. 4-digit number + 2-digit number gives a 4-digit number: SometimesNeverAlways true

c. 4-digit number + 2-digit number gives a 6-digit number : Never trueAlways true

d. 5-digit number – 5-digit number gives a 5-digit number : SometimesNeverAlways true

e. 5-digit number – 2-digit number gives a 3-digit number: Never trueAlways true