Today’s SAT question of the day is an arithmetic question that can be solved successfully in two ways: the long way and the short way.

The question starts like this:

To proceed the long way:

1. Multiply all of your numerators together (1 * 2 * 3 * 4 * 5 * 6 = 720)
2. Multiply all of your denominators together (2 * 3 * 4 * 5 * 6 * 7 = 5040)
3. Divide (720/5040 = .143 or 1/7, which you can get by using math > frac on your calculator)

To proceed the short way:

1. Stop and marvel at the fact that almost all of your numerators have a counterpart in the denominators.  Since x / x = 1, we can do a lot of canceling here and get this question solved without multiplying a single number.
2. Cancel everything that appears in both the numerator and denominator: 2, 3, 4, 5, 6.  This leaves just 1 and 7, or 1/7.
3. Take the time you just saved and move on to the next question.

Key terms and concepts to remember:

• numerator: the top number in a fraction
• denominator: the bottom number in a fraction – remember that it’s the “down” one because it starts with d
• canceling: why multiply if you’re just going to divide later?  Cancel whenever possible before performing any operations.