From time to time, we get lucky and the computation we have to do can be solved using a specific technique or trick that allows us to do effortless **mental math**.

**Level 1:**

12 x 125 = _______

The trick to this question is to see that "12" can be broken down into "3 x 4."

Think of "12 x 125" as "3 x (4 x 125)."

Now 4 x 125 = 500. (4 x 100 + 4 x 25)

Then, 3 x 500 = **1,500**.

*Try this (mentally)*: 8 x 175 = ________.

**Level 2:**

1/5 + 1/6 = __________

When you add two fractions, and the numerators of the fractions are both 1, the numerator of the answer is the *sum* of the denominators, and the denominator of the answer is the* product* of the denominators. In this problem, the numerator is (5 + 6), and the denominator is (5 x 6).

So, 1/5 + 1/6 = **11/30**. [Note: If the denominators are not *relatively prime*, the answer will have to be reduced.]

*Try this (mentally): *1/12 + 1/13 = _____________.

**Level 3:**

2,000 ÷ 16 = ____________

The trick here is to recognize that 16 is a power of 2, and that powers of 2 make division into "half-of-a-half-of-a..."

In this case, since 16 is "2 to the fourth power," we simply cut 2,000 in half 4 times.

So,

Half of 2,000 is 1,000,

Half of 1,000 is 500,

Half of 500 is 250, and finally,

Half of 250 is 125.

So, 2,000 ÷ 16 = **125**.

*Try this (mentally)*: 3,000 ÷ 8 = ____________.

**Note that there is more than one trick for each of these questions. See if you can find others!**