Write down your first ratio as a fraction. If you want to determine the chances of winning a lottery or a raffle, record the chances of winning the lottery as a fraction. If those chances are described as a million to one, write 1/1,000,000.
Write down your second ratio as a fraction. To continue the first example, your second ratio would describe the chances of winning the raffle. If those chances are written as one to one thousand, write 1/1,000.
Multiply the nominator, the top number, of the first ratio with the denominator, the bottom number of the second ratio. In our example, we would multiply 1 by 1,000. Multiply the second ratio's nominator by the first ratio's denominator (1 by 1,000,000). Add the products together (1,000 + 1,000,000 = 1,001,000). The resulting sum is the numerator of the final ratio.
Multiply the first ratio's denominator by the second ratio's denominator (1,000,000 by 1,000). The resulting number (1,000,000,000) is the final ratio's denominator.
Combine the final ratio's numerator and denominator. In the above example, we conclude that the chances of winning either the raffle or the lottery are 1,001,000 to 1,000,000,000, or approximately 1 to 999.