House of Hundreds - I — NCERT Solutions

Concept: Locating numbers on a number line between 400 and 500.

• 423 — 23 steps after 400, close to 400.
• 438 — 38 steps after 400, between 423 and 450.
• 476 — 76 steps after 400, between 450 and 487.
• 487 — 87 steps after 400, close to 500.
• 500 — at the end of the number line.

$$400 \quad \ldots \quad 423 \quad \ldots \quad 438 \quad \ldots \quad 476 \quad \ldots \quad 487 \quad \ldots \quad 500$$

Mark all numbers at their correct positions on the number line.

Concept: House numbers in an apartment follow a pattern.

Pattern observed:

• Each floor has 10 houses (columns 1–10).
• Ground floor (1st floor): Houses 1–10; 2nd floor: 11–20; 3rd floor: 21–30, and so on.
• Moving left to right: house number increases by 1.
• Moving up one floor: house number increases by 10.

Fill the grid using this pattern:

Continue the pattern to fill all blank cells.

Concept: Locating specific house numbers in the apartment grid.

Method: Find each house number in the grid and colour it.

• Identify the floor and column for each number using the pattern:
• Floor = $\lceil \text{house number} \div 10 \rceil$
• Column = last digit (if last digit = 0, column = 10)

Locate and colour: 209, 228, 242, 258, 267, 276, 290, 315, 346, 367, 389, 395.

(Find each number in the grid and colour it.)

Concept: Floor = tens digit + 1 (if ones digit ≠ 0) or tens digit (if ones digit = 0). Column = ones digit (0 means column 10).

Rule:

• If house number ends in 0: Floor = house number ÷ 10, Column = 10
• Otherwise: Floor = (house number ÷ 10) rounded down + 1, Column = ones digit

(Note: Floor numbering follows the apartment grid pattern shown in the figure. Adjust if the grid starts differently.)

Concept: Pattern in house numbers in the apartment building.

Observations:

• Moving left to right (same floor): house number increases by 1.
• Moving right to left (same floor): house number decreases by 1.
• Moving up (same column): house number increases by 10.
• Moving down (same column): house number decreases by 10.

Fill the blanks using these rules:

• If a house to the right is 245, the house to its left is $245 - 1 = 244$.
• If a house above is 245, the house below is $245 - 10 = 235$.

Pattern noticed: House numbers increase by 1 going right and by 10 going up.

(i) Given: Digits are 9, 1, 5; less than 200; has 9 ones.

• Less than 200 → hundreds digit = 1
• 9 ones → ones digit = 9
• Remaining digit = 5 → tens digit = 5

$$\text{Number} = 1 \text{ hundred} + 5 \text{ tens} + 9 \text{ ones} = \mathbf{159}$$

(ii) Given: 3-digit number using only digits 4 and 0.

• Possible numbers: 400, 404, 440, 444, 400…
• The most likely answer (using only 4 and 0): 400 (4 hundreds, 0 tens, 0 ones)

$$\text{Number} = \mathbf{400}$$

(iii) Given: Greater than 300 but less than 400; no tens; ones digit = hundreds digit.

• Hundreds digit = 3 (since between 300 and 400)
• Tens digit = 0 (no tens)
• Ones digit = hundreds digit = 3

$$\text{Number} = 3 \text{ hundreds} + 0 \text{ tens} + 3 \text{ ones} = \mathbf{303}$$

Concept: Representing a number using Hundreds (H), Tens (T), and Ones (O) boxes.

Rule: Break the number into hundreds, tens, and ones.

Draw the corresponding number of H boxes, T boxes, and O packets for each house number.

Concept: Reading house numbers from the apartment grid.

(The exact house numbers depend on the figure. Identify the yellow and pink coloured houses in the grid and write their numbers.)

Method: Locate each coloured house in the grid and read its number using the floor and column pattern.

Concept: Identifying number patterns.

Possible patterns to look for:

• Do the numbers increase by the same amount each time?
• Are they all even or all odd?
• Do they share a common digit?

Example pattern: If yellow houses are 211, 221, 231, 241 — they increase by 10 each time (same column, going up).

Write the pattern observed from the actual numbers in the figure.

Given: 1 box of 100 sweets; each small box holds 10 sweets.

$$100 \div 10 = \mathbf{10}$$

He can fit 10 boxes of 10 in a box of 100.

Given: 2 boxes of 100.

$$2 \times 10 = \mathbf{20}$$

He can fit 20 boxes of 10 in two boxes of 100.

Given: 4 boxes of 100.

$$4 \times 10 = \mathbf{40}$$

He can fit 40 boxes of 10 in four boxes of 100.

Given: 1 box of 100 is opened.

$$100 \div 10 = \mathbf{10}$$

He will find 10 boxes of 10 inside a box of 100.

Concept: Finding all numbers between 200 and 300 that contain the digit 5.

Numbers between 200 and 300 with digit 5:

• 5 in the tens place: 250, 251, 252, 253, 254, 255, 256, 257, 258, 259
• 5 in the ones place: 205, 215, 225, 235, 245, 255, 265, 275, 285, 295

Complete list (no repeats):
$$205, 215, 225, 235, 245, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 265, 275, 285, 295$$

Yes, 245 is one such number (it has 5 in the ones place).

Total: 19 numbers between 200 and 300 have the digit 5.

Concept: Comparing 3-digit numbers — first compare hundreds, then tens, then ones.

Method:

1. Compare hundreds digits first.
2. If equal, compare tens digits.
3. If equal, compare ones digits.

(The exact numbers depend on the figure. Apply the method above.)

Example: Compare 321 and 231:

• Hundreds: 3 > 2
• So $321 > 231$ ✓

Concept: Comparing 3-digit numbers.

Example: Compare 209 and 290:

• Hundreds: both have 2 (equal)
• Tens: 0 < 9
• So $209 < 290$ ✓

(Apply the same method to the numbers shown in the figure.)

Concept: Comparing numbers by hundreds, tens, and ones.

(a) 325 > 235 because → 325 has 3 hundreds and 235 has 2 hundreds. 3 hundreds > 2 hundreds.

(b) 235 < 523 because → 235 has 2 hundreds and 523 has 5 hundreds. 2 hundreds < 5 hundreds.

(c) 157 > 153 because → Both have 1 hundred and 5 tens each. 157 has 7 ones, 153 has 3 ones. 7 ones > 3 ones.

(d) 432 > 423 because → Both have 4 hundreds. 432 has 3 tens, 423 has 2 tens. 3 tens > 2 tens.

(e) 329 < 392 because → Both have 3 hundreds. 329 has 2 tens, 392 has 9 tens. 2 tens < 9 tens.

(f) 110 > 11 because → 110 has 1 hundred and 11 has no hundreds (zero hundreds). 1 hundred > 0 hundreds.

Concept: Finding the smallest number by comparing hundreds first, then tens, then ones.

(a) 374, 473, 347, 437

• All have 3 or 4 in hundreds place.
• Numbers with 3 hundreds: 374, 347 → compare tens: 7 vs 4 → 347 is smaller.
• Numbers with 4 hundreds: 473, 437 → all larger than 3xx.
• Smallest = 347 ✓

$$\boxed{347}$$

(b) 239, 123, 321, 456

• Hundreds digits: 2, 1, 3, 4
• Smallest hundreds digit = 1 → number is 123

$$\boxed{123}$$

Concept: Finding the greatest number by comparing hundreds first, then tens, then ones.

(a) 466, 437, 439, 447, 483

• All have 4 hundreds.
• Compare tens: 6, 3, 3, 4, 8 → greatest tens = 8 → number is 483

$$\boxed{483}$$

(b) 464, 387, 123, 256, 348

• Hundreds digits: 4, 3, 1, 2, 3
• Greatest hundreds digit = 4 → number is 464

$$\boxed{464}$$

Given digits: 3, 2, 4 (each used exactly once)

All possible 3-digit numbers:
$$234, 243, 324, 342, 423, 432$$

Greatest number: $\mathbf{432}$ → colour red

Smallest number: $\mathbf{234}$ → colour yellow

All six numbers: 234, 243, 324, 342, 423, 432

Given digits: 3, 2, 4 (repetition allowed)

Some possible 3-digit numbers (sample):
$$222, 223, 224, 232, 233, 234, 242, 243, 244,$$
$$322, 323, 324, 332, 333, 334, 342, 343, 344,$$
$$422, 423, 424, 432, 433, 434, 442, 443, 444$$

Greatest number: $\mathbf{444}$ → colour red

Smallest number: $\mathbf{222}$ → colour yellow

(Write as many numbers as possible using digits 2, 3, 4 with repetition allowed.)

Concept: Arranging numbers in ascending order.

Step 1: Compare hundreds digits.

• 99 has no hundreds (2-digit number) → smallest
• 110 has 1 hundred
• 207 has 2 hundreds
• 389 has 3 hundreds
• 456 has 4 hundreds

Ascending order (smallest to biggest):
$$\mathbf{99 < 110 < 207 < 389 < 456}$$

Concept: Arranging numbers in descending order.

Step 1: Compare hundreds digits.

• 67 has no hundreds (2-digit) → smallest
• 249 has 2 hundreds
• 294 has 2 hundreds → compare tens: 4 < 9, so 249 < 294
• 376 has 3 hundreds
• 494 has 4 hundreds → greatest

Descending order (biggest to smallest):
$$\mathbf{494 > 376 > 294 > 249 > 67}$$