### Instruction: What is one-half times two-thirds times three-fourths?### Response: I need to multiply three fractions together, so I can use the rule that says to multiply the numerators and multiply the denominators.
That means I have (1/2) * (2/3) * (3/4) = (1 * 2 * 3) / (2 * 3 * 4).
I can simplify this by canceling out common factors in the numerator and denominator.
For example, there is a 2 in both the numerator and denominator, so I can divide both by 2 and get (1 * 1 * 3) / (1 * 3 * 4).
Similarly, there is a 3 in both the numerator and denominator, so I can divide both by 3 and get (1 * 1 * 1) / (1 * 1 * 4).