What is the standard notation for a ratio?

• A. a/b, a to b, or a:b (where b is not zero)
• B. a+b, a to b, or a:b
• C. a/b, b/a, or a:b (where a is not zero)
• D. a:b, a to b, or a:b (b is zero)

Answer: (A)

A ratio is a way of comparing two quantities, and the standard notations are a/b, spoken as “a to b,” or written as a:b. The important rule is that the second number, b, cannot be zero, because division by zero is undefined. For example, if a = 3 and b = 4, 3/4, “3 to 4,” and 3:4 all express the same ratio.

One option uses a+b, which is addition and not a way to express a ratio. Another option incorrectly says the numerator can’t be zero, but zero can be the top number in a ratio (0/b = 0 when b ≠ 0). Another option says the denominator could be zero, which would make the expression undefined. So the correct form is the one that lists the three valid notations and notes that the denominator must not be zero.