Question

how many integers are neither multiples of 3 nor multiples of 5?

Answer 1

Answer:

Get a sheet of squared paper, say with 1cm squares (although the size does not matter) . Draw a large square 10cm x 10cm. That will enclose 100 smaller squares. Call the top left square 1, the rightmost square in the top row 10, and so on until you reach the bottom right square, which will be 100.

From the top left (square number 1) count 3 squares across (including the first). That will be square number 3, obviously. Make a cross. Repeat, moving across by 3 and wrapping round at the end of the row, making a cross every third square. The last square you mark will be the one next to the bottom right one, i.e. 99. Then you will have marked all of the multiples of three between one and a hundred.