What are the multiples of 9 up to 1000?

Steps to Solve

1. Identify the first multiple of 9 The first multiple of 9 is simply 9 multiplied by 1.

$9 \times 1 = 9$

2. Identify the last multiple of 9 within the range Next, we need to find the largest integer ( n ) such that ( 9n \leq 1000 ). To do this, we can divide 1000 by 9.

$$ n = \left\lfloor \frac{1000}{9} \right\rfloor $$

Calculating that gives:

$$ n \approx 111.11 \implies n = 111 $$

3. List all multiples of 9 Now that we have determined that the largest integer ( n ) is 111, we can find all the multiples of 9 from 1 to 111. The multiples of 9 can be represented as:

$$ 9, 18, 27, \ldots, 9n $$

Thus:

$$ 9 \times 1, 9 \times 2, \ldots, 9 \times 111 $$

4. Write down the multiples Calculating the multiples of 9 yields:

The multiples are:

$$ 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 495, 504, 513, 522, 531, 540, 549, 558, 567, 576, 585, 594, 603, 612, 621, 630, 639, 648, 657, 666, 675, 684, 693, 702, 711, 720, 729, 738, 747, 756, 765, 774, 783, 792, 801, 810, 819, 828, 837, 846, 855, 864, 873, 882, 891, 900, 909, 918, 927, 936, 945, 954, 963, 972, 981, 990, 999$$