Looking Back. The Venn diagram helps to answer other questions. How many numbers less than or equal to 300 are multiples of 3 but not multiples of 5?
To solve this problem, we can create a Venn diagram with two overlapping circles representing multiples of 3 and multiples of 5.
Let's consider the multiples of 3 first. The first multiple of 3 less than or equal to 300 is 3, and the last multiple is 300. To find the number of multiples of 3 in this range, we divide 300 by 3 and round down to the nearest whole number: ⌊300/3⌋ = 100. So, there are 100 multiples of 3 less than or equal to 300.
Now, let's consider the multiples of 5. The first multiple of 5 less than or equal to 300 is 5, and the last multiple is 300. To find the number of multiples of 5 in this range, we divide 300 by 5 and round down to the nearest whole number: ⌊300/5⌋ = 60. So, there are 60 multiples of 5 less than or equal to 300.
To find the numbers that are multiples of 3 but not multiples of 5, we need to subtract the common multiples (multiples of both 3 and 5) from the total number of multiples of 3.
To determine the common multiples, we can find the multiples of 15 (the smallest common multiple of 3 and 5) less than or equal to 300. The first multiple of 15 is 15, and the last multiple is 300. Dividing 300 by 15 and rounding down gives us ⌊300/15⌋ = 20. So, there are 20 common multiples of 3 and 5.
Now we can calculate the number of numbers that are multiples of 3 but not multiples of 5 by subtracting the number of common multiples from the total number of multiples of 3: 100 - 20 = 80.
Therefore, there are 80 numbers less than or equal to 300 that are multiples of 3 but not multiples of 5.