5. How many positive integers less than 36 are equal to 4 times an odd integers?
4 * 1
4 * 3
4 * 5
4 * 7
4
To find the positive integers less than 36 that are equal to 4 times an odd integer, we can proceed step-by-step:
Step 1: Find the odd integers less than 36:
The odd integers less than 36 are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, and 33.
Step 2: Multiply each odd integer by 4:
1 x 4 = 4
3 x 4 = 12
5 x 4 = 20
7 x 4 = 28
9 x 4 = 36
11 x 4 = 44
13 x 4 = 52
15 x 4 = 60
17 x 4 = 68
19 x 4 = 76
21 x 4 = 84
23 x 4 = 92
25 x 4 = 100
27 x 4 = 108
29 x 4 = 116
31 x 4 = 124
33 x 4 = 132
Step 3: Identify the positive integers less than 36:
Among these results, only 4, 12, 20, 28 are positive integers less than 36 that are equal to 4 times an odd integer.
Therefore, there are 4 positive integers less than 36 that are equal to 4 times an odd integer.
To find the number of positive integers less than 36 that are equal to 4 times an odd integer, we need to divide the given range into two parts: one for odd integers and the other for their corresponding values when multiplied by 4.
1. Finding the odd integers: We know that odd numbers are integers that are not divisible by 2. In the range from 1 to 36, we have odd numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, and 33.
2. Finding their corresponding values when multiplied by 4: Multiply each odd number by 4 to find their corresponding values. The products are 4, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, and 132.
3. Counting the positive integers less than 36: From the list above, we can see that only five numbers (4, 12, 20, 28, and 36) are less than 36 and equal to 4 times an odd integer.
Therefore, there are 5 positive integers less than 36 that are equal to 4 times an odd integer.