To find the integers between 100 and 500 that are multiples of 11, we first need to identify the smallest and largest multiples of 11 within this range.
The smallest multiple of 11 that is greater than or equal to 100 can be found by dividing 100 by 11 and rounding up to the nearest whole number:
- 100 ÷ 11 ≈ 9.09
- Rounding up gives us 10.
Now, multiply this whole number by 11:
- 10 × 11 = 110
So, the smallest multiple of 11 that is at least 100 is 110.
Next, we find the largest multiple of 11 that is less than or equal to 500:
- 500 ÷ 11 ≈ 45.45
- Rounding down gives us 45.
Now, multiply this whole number by 11:
- 45 × 11 = 495
This means the largest multiple of 11 that is at most 500 is 495.
Now we need to find all the multiples of 11 from 110 to 495. The multiples of 11 can be expressed as:
- 11 × n
where n is an integer. The values of n for our range are:
- From 10 (for 110) to 45 (for 495).
To find the total number of integers, we subtract the two values:
- 45 – 10 + 1 = 36.
Thus, the total number of integers between 100 and 500 that are multiples of 11 is 36.