Based on the Creative Chitti section on page 6 of the textbook, Chitti is a calculator with buttons for large place values (+1, +10, +100, +1,000, +10,000, +1,00,000, and +10,00,000). It loves to find creative, alternative ways to break down numbers instead of just using standard place values.

Here are solutions for the "Figure it Out" exercises by writing expressions for at least two different creative ways to obtain each number:

(a) 8300

Way 1 (Splitting into Thousands and Hundreds): We can press the +1,000 button 8 times and the +100 button 3 times.
$\text{Expression: } (8 \times 1000) + (3 \times 100) = 8300$
Way 2 (Using only Hundreds): We can lean completely on the hundreds button and press +100 exactly 83 times.
$\text{Expression: } 83 \times 100 = 8300$

(b) 40629

Way 1 (Standard-ish Breakdown): Press +10,000 four times, +100 six times, +10 two times, and +1 nine times.
$\text{Expression: } (4 \times 10000) + (6 \times 100) + (2 \times 10) + (9 \times 1) = 40629$
Way 2 (Shifting Tens to Ones): Instead of using the tens button, we can convert those two tens into 29 ones. Press +10,000 four times, +100 six times, and +1 twenty-nine times.
$\text{Expression: } (4 \times 10000) + (6 \times 100) + (29 \times 1) = 40629$

(c) 56354

Way 1 (Grouping Thousands together): Instead of using the ten-thousands button, let's look at the first part as 56 thousands. Press +1,000 fifty-six times, +100 three times, +10 five times, and +1 four times.
$\text{Expression: } (56 \times 1000) + (3 \times 100) + (5 \times 10) + (4 \times 1) = 56354$
Way 2 (Grouping Hundreds and Tens): Press +10,000 five times, +1,000 six times, and combine the rest into 354 ones. Press +1 exactly 354 times.
$\text{Expression: } (5 \times 10000) + (6 \times 1000) + (354 \times 1) = 56354$

(d) 66666

Way 1 (The "All Sixes" Method): Press each respective place value button exactly 6 times.
$\text{Expression: } (6 \times 10000) + (6 \times 1000) + (6 \times 100) + (6 \times 10) + (6 \times 1) = 66666$
Way 2 (The Heavy Hundreds Method): Press +10,000 six times, +1,000 six times, and press the +100 button sixty-six times to cover the remaining $6600$ , plus 6 ones.
$\text{Expression: } (6 \times 10000) + (6 \times 1000) + (66 \times 100) + (6 \times 1) = 66666$

(e) 367813

Way 1 (Lakhs and Thousands Breakdown): Press +1,00,000 three times, +10,000 six times, +1,000 seven times, +100 eight times, and +1 thirteen times.
$\text{Expression: } (3 \times 100000) + (6 \times 10000) + (7 \times 1000) + (8 \times 100) + (13 \times 1) = 367813$
Way 2 (Massive Thousands Grouping): Treat the front of the number as 367 thousands. Press +1,000 exactly 367 times, +10 eighty-one times ( $81 \times 10 = 810$ ), and +1 three times.
$\text{Expression: } (367 \times 1000) + (81 \times 10) + (3 \times 1) = 367813$

Creative Chitti's Bonus Questions (Bottom of page 6 / Top of page 7)

(a) You have to make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest 3-digit number you can make?

Largest 3-digit number: To make the number as large as possible, we want to maximize the hundreds place. However, the largest standard digit is 9. Because Chitti lets us overload buttons creatively, we can press +100 twenty-eight times ( $28 \times 100 = 2800$ , which becomes a 4-digit number, so that's too big!).
To keep it strictly a 3-digit number, the maximum hundreds we can have is 9.
- Press +100 $\rightarrow$ 9 times (900)
- Press +10 $\rightarrow$ 21 times (210)
- Total clicks = $9 + 21 = 30$ clicks.
- Result: $900 + 210 =$ 1110 (Wait, that's a 4-digit number!).
Let's adjust it so the final sum stays under 1000:
- Press +100 $\rightarrow$ 9 times (900)
- Press +10 $\rightarrow$ 9 times (90)
- Press +1 $\rightarrow$ 12 times (12)
- Total clicks = $9 + 9 + 12 = 30$ clicks.
- Largest 3-digit sum: $900 + 90 + 12 =$ 999 is the limit for a 3-digit number (using 9 hundreds clicks, 8 tens clicks, and 13 ones clicks, etc.).
Smallest 3-digit number: To keep it as small as possible but still a 3-digit number (at least 100), we want to use the smallest values (+1) as much as possible.
- Press +1 $\rightarrow$ 29 times (29)
- Press +100 $\rightarrow$ 1 time (100)
- Total clicks = $29 + 1 = 30$ clicks.
- Smallest 3-digit sum: $100 + 29 =$ 129

(b) 997 can be made using 25 clicks. [i.e., $(9 \times 100) + (9 \times 10) + (7 \times 1) = 25$ clicks]. Can you make 997 with a different number of clicks?

Yes! For example, instead of pressing +10 nine times, we can break one of those tens down into ten +1 clicks.

Press +100 nine times, +10 eight times, and +1 seventeen times.
$\text{Expression: } (9 \times 100) + (8 \times 10) + (17 \times 1) = 997$
New total clicks: $9 + 8 + 17 =$ 34 clicks.

(a) With exactly 30 button presses:

Largest 3-digit number you can make: 999
- How to get it: To keep it a 3-digit number while using up all 30 clicks, we can max out the hundreds and tens places, and dump the remaining clicks into the ones place.
- Press +100 $\rightarrow$ 9 times ( $9 \times 100 = 900$ )
- Press +10 $\rightarrow$ 9 times ( $9 \times 10 = 90$ )
- Press +1 $\rightarrow$ 12 times ( $12 \times 1 = 12$ )
- Total Clicks: $9 + 9 + 12 = 30$ clicks.
- Expression: $(9 \times 100) + (9 \times 10) + (12 \times 1) = 900 + 90 + 12 = 1002$ (Wait, 1002 is a 4-digit number! Let's correct the strategy to ensure the final value stays strictly under 1,000).
- Correct Strategy for 999: * Press +100 $\rightarrow$ 9 times ( $900$ )
  - Press +10 $\rightarrow$ 8 times ( $80$ )
  - Press +1 $\rightarrow$ 13 times ( $13$ )
  - Total Clicks: $9 + 8 + 13 = 30$ clicks.
  - Expression: $(9 \times 100) + (8 \times 10) + (13 \times 1) = 900 + 80 + 13 =$ 999
Smallest 3-digit number you can make: 129
- How to get it: To keep the number as small as possible, we want to use the lowest value button (+1) as many times as we can, and only use a higher button once to cross into 3-digit territory (100 or more).
- Press +100 $\rightarrow$ 1 time ( $1 \times 100 = 100$ )
- Press +1 $\rightarrow$ 29 times ( $29 \times 1 = 29$ )
- Total Clicks: $1 + 29 = 30$ clicks.
- Expression: $(1 \times 100) + (29 \times 1) = 100 + 29 =$ 129

(b) Making 997 with a different number of clicks:

Yes, you can absolutely make 997 with a different number of clicks! The textbook shows the standard way uses 25 clicks: $(9 \times 100) + (9 \times 10) + (7 \times 1) = 25$ clicks. By breaking down larger place values into smaller ones, we can change the total click count. Here are two creative alternatives:

Alternative 1 (Using 34 clicks): Instead of pressing +10 nine times, press it 8 times and convert that 1 missing ten into ten individual +1 clicks.
- $\text{Expression: } (9 \times 100) + (8 \times 10) + (17 \times 1) = 997$
- Total Clicks: $9 + 8 + 17 =$ 34 clicks
Alternative 2 (Using 106 clicks): We can skip the +100 button entirely and build the number out of tens and ones.

$\text{Expression: } (99 \times 10) + (7 \times 1) = 997$
Total Clicks: $99 + 7 =$ 106 clicks

Systematic Sippy is a calculator that wants to be used as minimally as possible. To get the target numbers using the fewest button clicks, we should use the standard place value breakdown (the Indian place value system notation).

Here are the solutions for the numbers from the previous exercise, broken down with the minimum number of clicks:

1. Smallest Number of Button Clicks for Each Number

(a) 5,072

To minimize clicks, look directly at the place values: 5 thousands, 0 hundreds, 7 tens, and 2 ones.

Expression:
$(5 \times 1,000) + (7 \times 10) + (2 \times 1) = 5,072$
Total Clicks: $5 + 0 + 7 + 2 =$ 14 clicks > Note: The textbook example on page 7 shows a way using 23 clicks, but notes that using the thousands place directly reduces it to 14 clicks!

(b) 8,300

Break it down into 8 thousands and 3 hundreds.

Expression:
$(8 \times 1,000) + (3 \times 100) = 8,300$
Total Clicks: $8 + 3 =$ 11 clicks

(c) 40,629

Break it down into 4 ten-thousands, 6 hundreds, 2 tens, and 9 ones.

Expression:
$(4 \times 10,000) + (6 \times 100) + (2 \times 10) + (9 \times 1) = 40,629$
Total Clicks: $4 + 0 + 6 + 2 + 9 =$ 21 clicks

(d) 56,354

Break it down into 5 ten-thousands, 6 thousands, 3 hundreds, 5 tens, and 4 ones.

Expression:
$(5 \times 10,000) + (6 \times 1,000) + (3 \times 100) + (5 \times 10) + (4 \times 1) = 56,354$
Total Clicks: $5 + 6 + 3 + 5 + 4 =$ 23 clicks

(e) 66,666

Press each matching place value button exactly 6 times.

Expression:
$(6 \times 10,000) + (6 \times 1,000) + (6 \times 100) + (6 \times 10) + (6 \times 1) = 66,666$
Total Clicks: $6 + 6 + 6 + 6 + 6 =$ 30 clicks

(f) 3,67,813

Break it down into 3 lakhs, 6 ten-thousands, 7 thousands, 8 hundreds, 1 ten, and 3 ones.

Expression:
$(3 \times 1,00,000) + (6 \times 10,000) + (7 \times 1,000) + (8 \times 100) + (1 \times 10) + (3 \times 1) = 3,67,813$
Total Clicks: $3 + 6 + 7 + 8 + 1 + 3 =$ 28 clicks

2. Follow-up Questions Answered

Question 2: Do you see any connection between each number and the corresponding smallest number of button clicks?

Answer: Yes! The smallest number of button clicks is always exactly equal to the sum of the individual digits of the number. For example, for $8,300$ , the sum of the digits is $8 + 3 + 0 + 0 = 11$ , which matches the 11 clicks.

Question 3: If you notice, the expressions for the least button clicks also give the Indian place value notation of the numbers. Think about why this is so.

Answer: This happens because our number system is based on groups of 10 (base-10). Each digit in a number tells us exactly how many bundles of that specific place value ( $1, 10, 100, 1,000,$ etc.) are needed. Since Systematic Sippy's buttons exactly match these standard place value units, using the exact digit amount avoids "overloading" smaller buttons, giving us the most efficient (minimal) way to build the number.

Based on page 7 of the NCERT Ganita Prakash Grade 6 textbook, Systematic Sippy is a calculator that wants to be used as minimally as possible. To get the target numbers using the fewest button clicks, we should use the standard place value breakdown (the Indian place value system notation).

Here are the solutions for the numbers from the previous exercise, broken down with the minimum number of clicks:

1. Smallest Number of Button Clicks for Each Number

(a) 5,072

To minimize clicks, look directly at the place values: 5 thousands, 0 hundreds, 7 tens, and 2 ones.

Expression:
$(5 \times 1,000) + (7 \times 10) + (2 \times 1) = 5,072$
Total Clicks: $5 + 0 + 7 + 2 =$ 14 clicks > Note: The textbook example on page 7 shows a way using 23 clicks, but notes that using the thousands place directly reduces it to 14 clicks!

(b) 8,300

Break it down into 8 thousands and 3 hundreds.

Expression:
$(8 \times 1,000) + (3 \times 100) = 8,300$
Total Clicks: $8 + 3 =$ 11 clicks

(c) 40,629

Break it down into 4 ten-thousands, 6 hundreds, 2 tens, and 9 ones.

Expression:
$(4 \times 10,000) + (6 \times 100) + (2 \times 10) + (9 \times 1) = 40,629$
Total Clicks: $4 + 0 + 6 + 2 + 9 =$ 21 clicks

(d) 56,354

Break it down into 5 ten-thousands, 6 thousands, 3 hundreds, 5 tens, and 4 ones.

Expression:
$(5 \times 10,000) + (6 \times 1,000) + (3 \times 100) + (5 \times 10) + (4 \times 1) = 56,354$
Total Clicks: $5 + 6 + 3 + 5 + 4 =$ 23 clicks

(e) 66,666

Press each matching place value button exactly 6 times.

Expression:
$(6 \times 10,000) + (6 \times 1,000) + (6 \times 100) + (6 \times 10) + (6 \times 1) = 66,666$
Total Clicks: $6 + 6 + 6 + 6 + 6 =$ 30 clicks

(f) 3,67,813

Break it down into 3 lakhs, 6 ten-thousands, 7 thousands, 8 hundreds, 1 ten, and 3 ones.

Expression:
$(3 \times 1,00,000) + (6 \times 10,000) + (7 \times 1,000) + (8 \times 100) + (1 \times 10) + (3 \times 1) = 3,67,813$
Total Clicks: $3 + 6 + 7 + 8 + 1 + 3 =$ 28 clicks

2. Follow-up Questions Answered

Question 2: Do you see any connection between each number and the corresponding smallest number of button clicks?

Question 3: If you notice, the expressions for the least button clicks also give the Indian place value notation of the numbers. Think about why this is so.

Here is a comprehensive study guide and revision material for Section 1.4: Exact and Approximate Values from your NCERT Ganita Prakash Grade 6 textbook.

📊 Study Material: Exact and Approximate Values (Section 1.4)

1. Core Concepts: Exact vs. Approximate

In daily life, science, and business, we deal with two types of numerical information depending on the situation:

Exact Values: These are precise counts that tell us exactly how many items are present. There is no guesswork or rounding involved.
- Example: The exact number of pages in a textbook chapter, or the number of students present in a classroom.
Approximate Values: These are "rough estimates" or "rounded numbers" used when a precise count is either impossible to get, unnecessary, or difficult to remember.
- Example: Saying "around 1 lakh people visited the book fair" instead of the exact ticket count of $99,542$ .

2. When to Round Up vs. Round Down

Approximation isn't just random guessing; it depends heavily on the practical scenario.

A. Situations for Rounding Up

Rounding up means making your approximate number larger than the actual number. We do this to ensure we have a safety margin or enough supplies.

Event Planning: If a school has 732 people (students, teachers, and staff), the principal orders 750 sweets instead of 700 so that no one runs out.
Travel Budgeting: If your train ticket costs ₹460, you might carry ₹500 just to be safe.

B. Situations for Rounding Down

Rounding down means making your approximate number smaller than the actual number. We often do this to simplify costs or give customer discounts.

Discounts/Estimating Expenses: If the bill for an item comes to ₹470, a friendly shopkeeper might tell you it costs around ₹450 to give you a quick discount.

C. Situations Requiring Exact Numbers

There are times when approximations are absolutely not allowed because even a small error can cause major issues:

Medicines: The dosage of a medicine must be exact (e.g., 5 ml or 500 mg).
Banking & Passwords: Bank account balances, PIN numbers, and phone numbers must always use exact digits.

3. Mastering "Nearest Neighbours" (Rounding Off)

A "nearest neighbour" is the closest multiple of 10, 100, 1,000, 10,000, Lakh, or Crore to a given number.

💡 General Rule of Thumb:

Look at the digit just to the right of the place value you want to round to:

If that digit is 5 or more (5, 6, 7, 8, 9) $\rightarrow$ Round UP (increase the target place value by 1, turn the rest to zeros).
If that digit is less than 5 (0, 1, 2, 3, 4) $\rightarrow$ Round DOWN (keep the target place value same, turn the rest to zeros).

Example from the Text:

Let's find the nearest neighbours for the number $6,72,85,183$:

Rounding Target	Digit to Check	Decision	Nearest Neighbour
Nearest Thousand	Look at Hundreds place ( $1$ )	Less than 5 $\rightarrow$ Round Down	`6,72,85,000`
Nearest Ten Thousand	Look at Thousands place ( $5$ )	5 or more $\rightarrow$ Round Up	`6,72,90,000`
Nearest Lakh	Look at Ten Thousands place ( $8$ )	5 or more $\rightarrow$ Round Up	`6,73,00,000`
Nearest Ten Lakh	Look at Lakhs place ( $2$ )	Less than 5 $\rightarrow$ Round Down	`6,70,00,000`
Nearest Crore	Look at Ten Lakhs place ( $7$ )	5 or more $\rightarrow$ Round Up	`7,00,00,000`

4. Textbook "Figure it Out" Exercises & Solutions

Test your skills using the problems from pages 11 and 12 of the NCERT Chapter 1 PDF:

Exercise 1: Find the 5 nearest neighbours

Write the nearest thousand, ten thousand, lakh, ten lakh, and crore for the following:

(a) 3,87,69,957

Nearest Thousand: 3,87,70,000 (Hundreds digit is 9, so 69,957 rounds up to 70,000)
Nearest Ten Thousand: 3,87,70,000 (Thousands digit is 9, so 60,000 rounds up to 70,000)
Nearest Lakh: 3,88,00,000 (Ten thousands digit is 6, so 7 lakhs rounds up to 8 lakhs)
Nearest Ten Lakh: 3,90,00,000 (Lakhs digit is 7, so 80 lakhs rounds up to 90 lakhs)
Nearest Crore: 4,00,00,000 (Ten Lakhs digit is 8, so 3 crore rounds up to 4 crore)

(b) 29,05,32,481

Nearest Thousand: 29,05,32,000 (Hundreds digit is 4 $\rightarrow$ Round down)
Nearest Ten Thousand: 29,05,30,000 (Thousands digit is 2 $\rightarrow$ Round down)
Nearest Lakh: 29,05,00,000 (Ten thousands digit is 3 $\rightarrow$ Round down)
Nearest Ten Lakh: 29,10,00,000 (Lakhs digit is 5 $\rightarrow$ Round up)
Nearest Crore: 29,00,00,000 (Ten Lakhs digit is 0 $\rightarrow$ Round down)

Exercise 2: Brain Teaser

"I have a number for which all five nearest neighbours are 5,00,00,000. What could the number be? How many such numbers are there?"

Thinking Process: For a number to round to $5,00,00,000$ across all categories (from thousands up to crores), its digits from the thousands place down to the ones place must already be exactly $0$ , and its outer boundaries must hover perfectly around 5 crores.
The Number could be: Exactly 5,00,00,000 itself!
How many such numbers? There is only 1 exact integer ( $5,00,00,000$ ) that stays perfectly unchanged at $5,00,00,000$ no matter which of those five place values you try to round it to.

Exercise 3: Estimating Sums (Roxie vs. Estu)

Problem: Estimate the value of $4,63,128 + 4,19,682$ .

Roxie says: "The sum is near 8,00,00,00 and is more than 8,00,000."
Estu says: "The sum is near 9,00,000 and is less than 9,00,000."

Solutions:

(a) Whose estimate is closer? Let's round to the nearest lakh to check: $4,63,128 \approx 5,00,00,00$ and $4,19,682 \approx 4,00,00,00$ . $5,00,000 + 4,00,000 = 9,00,000$ . Estu’s estimate is closer because the true sum is much closer to $9,00,00,00$ than $8,00,00,00$ .
(b) Will the sum be greater or less than 8,50,000?
Greater than 8,50,000. Even if you just add the leading lakhs ( $4,00,00,00 + 4,00,00,00 = 8,00,00,00$ ), the remaining parts ( $63,128 + 19,682$ ) easily cross $80,000$ , pushing the total past $8,80,000$ .
(c) Exact Value:
$4,63,128 + 4,19,682 = \mathbf{8,82,810}$

Here are the step-by-step solutions to the problems from page 11 and 12 of your NCERT Ganita Prakash Grade 6 textbook:

Given Problem:

Evaluate the estimation for:

14,63,128 - 4,90,020

Roxie's Estimate: "The difference is near $10,00,000$ and is less than $10,00,000$ ."
Estu's Estimate: "The difference is near $9,00,00,00$ and is more than $9,00,000$ ."

Solutions:

(a) Are these estimates correct? Whose estimate is closer to the difference?

Are they correct? Yes, both estimates are logically correct interpretation methods depending on how you round off. If we round to the nearest ten lakh, it is close to $10,00,000$ . If we look at the leading digits ( $14 \text{ lakhs} - 5 \text{ lakhs}$ ), it is close to $9,00,00,00$ .
Wholesale Closer: Estu's estimate is closer. * Why? If you quickly check the lakhs: $14,00,00,00 - 4,00,00,00 = 10,00,00,00$ . But since you are subtracting almost an extra lakh (subtracted value is $4,90,020$ , which is very close to $5,00,000$ ), the answer will drop down significantly below $10,00,00,00$ , landing much closer to $9,00,00,00$ ( $9.73 \text{ lakhs}$ ).

(b) Will the difference be greater than 9,50,000 or less than 9,50,000? Why do you think so?

Answer: Greater than 9,50,000.
Why? Think of it by rounding the numbers to simpler values: $14,63,128$ is well over $14.5 \text{ lakhs}$ (it's around $14,60,000$ ). Even if you subtract a full $5,00,000$ (which is larger than $4,90,020$ ), your answer would be $14,60,000 - 5,00,00,00 = 9,60,00,00$ . Since $9,60,00,00$ is greater than $9,50,00,00$ , the final difference must be greater than $9,50,00,00$ .

(c) Will the difference be greater than 9,63,128 or less than 9,63,128? Why do you think so?

Answer: Greater than 9,63,128.
Why? Let's look at the baseline math:
$14,63,128 - 5,00,000 = 9,63,128$
Because the number we are actually subtracting ( $4,90,020$ ) is less than $5,00,00,00$ , we are taking away less than a full 5 lakhs. When you subtract a smaller amount, your final remainder stays greater than the baseline value. Therefore, the result must be greater than $9,63,128$ .

(d) Exact value of 14,63,128 – 4,90,020 = __________

Calculation:
$\begin{array}{r@{\quad}l} 14,63,128 \\ -\phantom{0}4,90,020 \\ \hline \mathbf{9,73,108} \end{array}$
Answer: 9,73,108 (which proves Estu was right about it being more than 9,00,000!)

Based on your progress through Chapter 1 of the NCERT Ganita Prakash Grade 6 textbook, the next section is Section 1.5: Patterns in Products.

Here is a comprehensive study and practice guide for this section to help you master the concepts!

🔢 Study Material: Patterns in Products (Section 1.5)

1. Core Concepts: The Multiplication Shortcuts

This section explores how to bypass long, tedious calculations by spotting mathematical relationships and converting tricky numbers (like $5$ , $25$ , or $125$ ) into simple fractions of base-10 numbers ( $10$ , $100$ , or $1000$ ).

A. The "Multiply by 5" Shortcut

Instead of multiplying a large even number by 5, you can think of 5 as half of 10.

\text{Formula: } \mathbf{X \times 5 = (X \div 2) \times 10}

Why it works: Multiplying by 10 and dividing by 2 is mathematically identical to multiplying by 5.
Textbook Example:
$116 \times 5 = (116 \div 2) \times 10 = 58 \times 10 = \mathbf{580}$

B. The "Multiply by 25" Shortcut

Instead of doing a two-row multiplication by 25, think of 25 as a quarter of 100.

\text{Formula: } \mathbf{X \times 25 = (X \div 4) \times 100}

Textbook Example:
$824 \times 25 = (824 \div 4) \times 100 = 206 \times 100 = \mathbf{20,600}$

C. The "Multiply by 125" Shortcut

Similarly, 125 can be written as an eighth of 1000.

\text{Formula: } \mathbf{X \times 125 = (X \div 8) \times 1000}

2. Textbook "Figure it Out" Exercises & Solutions

Test your mental math skills using the problems straight from page 14 of the textbook:

Exercise 1: Quick Calculation Techniques

(a) $2 \times 1768 \times 50$

Shortcut: Rearrange the numbers to group $2$ and $50$ together first ( $2 \times 50 = 100$ ).
Calculation: $1768 \times (2 \times 50) = 1768 \times 100$
Answer: 1,76,800

(b) $72 \times 125$

Shortcut: Use the hint that $125 = \frac{1000}{8}$ . First, divide 72 by 8.
Calculation: $(72 \div 8) \times 1000 = 9 \times 1000$
Answer: 9,000

(c) $125 \times 40 \times 8 \times 25$

Shortcut: Group the friendly pairs together. Pair $125$ with $8$ ( $125 \times 8 = 1000$ ), and pair $40$ with $25$ ( $40 \times 25 = 1000$ ).
Calculation: $(125 \times 8) \times (40 \times 25) = 1000 \times 1000$
Answer: 10,00,000 (Ten Lakhs)

Exercise 2: Rapid Fire Products

(a) $25 \times 12 = $ 300 (Think: $(12 \div 4) \times 100 = 3 \times 100$ )
(b) $25 \times 240 = $ 6,000 (Think: $(240 \div 4) \times 100 = 60 \times 100$ )
(c) $250 \times 120 = $ 30,000 (Think: $25 \times 12 \times 100 = 300 \times 100$ )
(d) $2500 \times 12 = $ 30,000 (Think: $25 \times 12 \times 100 = 300 \times 100$ )
(e) Fill in the blanks: 25,000 $\times$ 4,800 $= 12,00,00,000$ (or any combination that balances the zeros and factors of 12)

3. Visual Patterns: "How Long is the Product?"

When you evaluate numbers made up entirely of repeating digits, beautiful visual symmetries emerge. Let's finish the patterns shown at the bottom of page 14:

Pattern A: The Pyramid of Ones

When multiplying strings of 1s by themselves, the answer counts up to the number of digits and then counts back down.

$11 \times 11 = \mathbf{121}$
$111 \times 111 = \mathbf{12,321}$
$1111 \times 1111 = \mathbf{12,34,321}$
Next in pattern: $11111 \times 11111 = \mathbf{123454321}$

Pattern B: The 6s and One 1

$66 \times 61 = \mathbf{4026}$
$666 \times 661 = \mathbf{4,40,226}$
$6666 \times 6661 = \mathbf{4,44,02,226}$
Next in pattern: $66666 \times 66661 = \mathbf{4444022226}$

Pattern C: The Threes and Fives

$3 \times 5 = \mathbf{15}$
$33 \times 35 = \mathbf{1,155}$
$333 \times 335 = \mathbf{1,11,555}$
Next in pattern: $3333 \times 3335 = \mathbf{1,11,15,555}$

Problem Type	Formula Ranges	Possible Number of Digits
1-digit $\times$ 1-digit	$(1+1-1)$ or $(1+1)$	1-digit or 2-digit (Given)
2-digit $\times$ 1-digit	$(2+1-1)$ or $(2+1)$	2-digit or 3-digit (Given)
2-digit $\times$ 2-digit	$(2+2-1)$ or $(2+2)$	3-digit or 4-digit (Given)
3-digit $\times$ 3-digit	$(3+3-1)$ or $(3+3)$	5-digit or 6-digit (Given)
5-digit $\times$ 5-digit	$(5+5-1)$ or $(5+5)$	9-digit or 10-digit
8-digit $\times$ 3-digit	$(8+3-1)$ or $(8+3)$	10-digit or 11-digit
12-digit $\times$ 13-digit	$(12+13-1)$ or $(12+13)$	24-digit or 25-digit

Search in Edunes

Part 2: Large Number Around Us Class 7 Mathematics

(a) 8300

(b) 40629

(c) 56354

(d) 66666

(e) 367813

Creative Chitti's Bonus Questions (Bottom of page 6 / Top of page 7)

(a) With exactly 30 button presses:

(b) Making 997 with a different number of clicks:

1. Smallest Number of Button Clicks for Each Number

(a) 5,072

(b) 8,300

(c) 40,629

(d) 56,354

(e) 66,666

(f) 3,67,813

2. Follow-up Questions Answered

1. Smallest Number of Button Clicks for Each Number

(a) 5,072

(b) 8,300

(c) 40,629

(d) 56,354

(e) 66,666

(f) 3,67,813

2. Follow-up Questions Answered

📊 Study Material: Exact and Approximate Values (Section 1.4)

1. Core Concepts: Exact vs. Approximate

2. When to Round Up vs. Round Down

A. Situations for Rounding Up

B. Situations for Rounding Down

C. Situations Requiring Exact Numbers

3. Mastering "Nearest Neighbours" (Rounding Off)

💡 General Rule of Thumb:

Example from the Text:

4. Textbook "Figure it Out" Exercises & Solutions

Exercise 1: Find the 5 nearest neighbours

Exercise 2: Brain Teaser

Exercise 3: Estimating Sums (Roxie vs. Estu)

Given Problem:

Solutions:

(a) Are these estimates correct? Whose estimate is closer to the difference?

(b) Will the difference be greater than 9,50,000 or less than 9,50,000? Why do you think so?

(c) Will the difference be greater than 9,63,128 or less than 9,63,128? Why do you think so?

(d) Exact value of 14,63,128 – 4,90,020 = __________

🔢 Study Material: Patterns in Products (Section 1.5)

1. Core Concepts: The Multiplication Shortcuts

A. The "Multiply by 5" Shortcut

B. The "Multiply by 25" Shortcut

C. The "Multiply by 125" Shortcut

2. Textbook "Figure it Out" Exercises & Solutions

Exercise 1: Quick Calculation Techniques

Exercise 2: Rapid Fire Products

3. Visual Patterns: "How Long is the Product?"

Pattern A: The Pyramid of Ones

Pattern B: The 6s and One 1

Pattern C: The Threes and Fives