Write an example for each of the scenarios shown in the diagram whenever possible.

Question

Homi · Accepted Answer

We will find an example for each scenario or explain why it is not possible.

Step 1 — First addition scenario

We need two 5-digit numbers. Their sum must be a 5-digit number. This sum must be more than 90,250.

$45,123 + 46,000$

$= 91,123$

$\boxed{45,123 + 46,000 = 91,123}$

Diagram 1

Step 2 — Second addition scenario

We need a 5-digit number and a 3-digit number. Their sum must be a 6-digit number.

$99,800 + 250$

$= 100,050$

$\boxed{99,800 + 250 = 100,050}$

Diagram 2

Step 3 — Third addition scenario

We need two 4-digit numbers. Their sum must be a 6-digit number. The largest 4-digit number is 9,999. The largest possible sum of two 4-digit numbers is 9,999 + 9,999 = 19,998. A 6-digit number must be at least 100,000. Since 19,998 is smaller than 100,000, this is not possible.

$\boxed{\text{Not possible}}$

Diagram 3

Step 4 — Fourth addition scenario

We need two 5-digit numbers. Their sum must be a 6-digit number.

$50,000 + 50,000$

$= 100,000$

$\boxed{50,000 + 50,000 = 100,000}$

Diagram 4

Step 5 — Fifth addition scenario

We need two 5-digit numbers. Their sum must be exactly 18,500. The smallest 5-digit number is 10,000. The smallest possible sum of two 5-digit numbers is 10,000 + 10,000 = 20,000. Since 18,500 is smaller than 20,000, this is not possible.

$\boxed{\text{Not possible}}$

Diagram 5

Step 6 — First subtraction scenario

We need two 5-digit numbers. Their difference must be less than 6,503.

$15,000 - 10,000$

$= 5,000$

$\boxed{15,000 - 10,000 = 5,000}$

Diagram 6

Step 7 — Second subtraction scenario

We need a 5-digit number and a 3-digit number. Their difference must be a 4-digit number.

$10,000 - 100$

$= 9,900$

$\boxed{10,000 - 100 = 9,900}$

Diagram 7

Step 8 — Third subtraction scenario

We need a 5-digit number and a 4-digit number. Their difference must be a 4-digit number.

$10,000 - 1,000$

$= 9,000$

$\boxed{10,000 - 1,000 = 9,000}$

Diagram 8

Step 9 — Fourth subtraction scenario

We need two 5-digit numbers. Their difference must be a 3-digit number.

$10,100 - 10,000$

$= 100$

$\boxed{10,100 - 10,000 = 100}$

Diagram 9

Step 10 — Fifth subtraction scenario

We need two 5-digit numbers. Their difference must be exactly 91,500. Let the first 5-digit number be $A$ and the second be $B$ . The largest 5-digit number is 99,999. The smallest 5-digit number is 10,000. The largest possible difference between two 5-digit numbers is 99,999 - 10,000 = 89,999. Since 91,500 is greater than 89,999, this is not possible.

$\boxed{\text{Not possible}}$

Diagram 10

Answer

(i) $45,123 + 46,000 = 91,123$ (ii) $99,800 + 250 = 100,050$ (iii) Not possible (iv) $50,000 + 50,000 = 100,000$ (v) Not possible (vi) $15,000 - 10,000 = 5,000$ (vii) $10,000 - 100 = 9,900$ (viii) $10,000 - 1,000 = 9,000$ (ix) $10,100 - 10,000 = 100$ (x) Not possible

Question 19

Answer

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