IB Mathematics SL Prep

Answer: C - 12 x $75 = $900. We could certainly figure this out by breaking up the 12 and multiplying 10 x $75 and adding that to 2 x $75 to reach the answer. However, it is much easier to calculate mentally by halving and doubling. This works fabulously when one of the numbers is even. In this case, our number 12 is even, so we will do the halving with that one, and we will do the doubling with 75.

12 x 75 is the same as 6 (which is 12 halved) x 150 (which is 75 doubled). This is the same as 3 (which is 6 halved) x 300 (which is 150 doubled). We can easily determine that 3x300 is 900. Those are much “friendlier” numbers to deal with than 12x75.

Key Takeaway: When multiplying two numbers together, and one of the numbers is even, use the halving and doubling technique to find friendlier numbers to multiply mentally. This takes a decent amount of practice. It also helps to know what numbers are friendly and unfriendly to you, and what number easily turn into friendly ones.