To determine how many multiples of 4 lie between 10 and 250, we can follow a few simple steps.
First, we need to find the smallest multiple of 4 that is greater than or equal to 10. We can do this by dividing 10 by 4:
10 ÷ 4 = 2.5
Since multiples must be whole numbers, we round up to the next whole number, which is 3. Now, we find the smallest multiple of 4:
4 × 3 = 12
Next, we find the largest multiple of 4 that is less than or equal to 250. Again, we divide:
250 ÷ 4 = 62.5
Here, we round down to the nearest whole number, which is 62. Now, we calculate the largest multiple of 4:
4 × 62 = 248
Now we have our range of multiples of 4, from 12 to 248. Next, we need to find out how many multiples of 4 fall within this range. The multiples of 4 can be represented by the equation:
4n, where n is an integer
So we solve for n when the smallest multiple is 12:
12 = 4n ⇒ n = 3
And for the largest multiple:
248 = 4n ⇒ n = 62
Now, we calculate the total number of multiples of 4 from n = 3 to n = 62:
62 - 3 + 1 = 60
Thus, the total number of multiples of 4 between 10 and 250 is 60.