October/November 2014 Newsflash: Tips & Techniques

Oct 16, 2014
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!

 

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