Cut it in half first!

My students are always looking for the easiest way to multiply numbers, especially since I don't allow them to depend on calculators.  Recently while learning how to find the area of triangles, I taught them to take advantage of the 1/2 in the formula, A = 1/2 x b x h.

Here's an example to consider.

Find the area of a triangle that has a base = 7, height = 18.  

Solution: A = 1/2 x b x h.  Plugging in the numbers, we see that A = 1/2 x 7 x 18.  Basic properties of math allow us to multiply the numbers in any order. 

Step 1: Multiply 18 x 1/2, or simply divide 18 by 2, which is 9.

Step 2:  Multiply 9 x 7, which = 63.

Done!  That was much easier than multiplying 7 x 18, then taking that product x 1/2!  Most people don't readily know that 7 x 18 = 126.  On the other hand, because we have learned our multiplication tables up to 10 x 10, we know that 7 x 9 = 63.

Let's try one more.

What is the product of 1/2 x 10 x 32?

Solution:  We have a choice to cut 10 or 32 in half, before multiplying the remaining number.  Which do you prefer?  Let's cut the 32 in half, so we can multiply the first product x 10.

Step 1:  Multiply 32 x 1/2 = 16.

Step 2: Multiply 16 x 10, which = 160.  All set!  We know that 1/2 x 10 x 32 = 160.

That was much easier than multiplying 1/2 x 10 = 5, then multiplying 5 x 32.

Remember that multiplying any number x 1/2 gives the same result as dividing that same number by 2..  There are many examples other than the finding area of triangles where you can use this helpful tip!