How do you get good at mental math?

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I used to be pretty good at it, now I am okay at it. I had to do 7.84/4 and felt pretty embarrassed that I couldn't do it.

1.96. Very easy. No odd remainders.

ruveyn

Ahh problem solved. Sense that was clearly what this topic was about.

By practicing, I try to do as much math in my head as possible, anything from adding up numbers, to division and even algebra at times. I like doing Net present value calculations in my head for instance.

you just need to drill. When you stopped practicing you will lose the talent. It's simply plasticity.

Practise is by far the most important aspect. Once you stop doing it, you automatically get worse.

Other than that, it helps to be aware of a few simple tricks. In the case of your example, the easiest way to compute the answer is by recognizing that 7.84 is close to 8 and then computing 0.16 / 4 and subtracting that from 2 (= 8 / 4) to obtain 2 - 0.04 = 1.96.

Keep doing it and find shortcuts you can use to solve it faster (128/4 = (120+8)/4 = ((12*10)+8)/4= ((3*10)+2)=32, would be one example. I separated 128 into a few smaller, easier to divide numbers, divided each by 4, and then recombined them)

Well 128 is just 2^7. Just looking at it I thought 32

That works too, but a lot of people have issues with exponents. Plus not everything is power of something, so this is a more general example. 128 is just the first number that popped into my mind.

Recently I discovered a memory saver for multiplying larger numbers.
The steps are as follows:

• Find the total number of digits for your working digits which is: S(sum of all digits) -1 = WD(working digits)
• Pick your multiplying number (preferably the one with the most digits)
• Multiply left to right
• Use the working digit formula to figure out where the chosen digit’s product goes
• Remember the working digits for each product
• Remember to add your carry overs

Example:
S1 -1 = WD1 = (3 + 3) - 1 = 5(Digits) or 10^4
S2 -1 = WD2 = (2 + 3) - 1 = 4(Digits) or 10^3
S3 -1 = WD3 = (1 + 3) - 1 = (2 + 2) -1 = 3(Digits) or 10^2
S4 - 1 = WD4 = (1 + 2) -1 = 2(Digits) or 10^1
S5 - 1 = WD5 = (1 + 1) -1 = 1(Digit) or 10^0
563 * 721=X
= (5 * 7)WD1 + (5 * 2)WD2 + (5 * 1)WD3 + (6 * 7)WD2 + (6 * 2)WD3 + (6 * 1)WD4 + (3 * 7)WD3 + (3 * 2)WD4 + (3 * 1)WD5

= (35)WD1 + (10)WD2 + (5)WD3 + (42)WD2 + (12)WD3 + (6)WD4 + (21)WD3 + (6)WD4 + (3)WD5

= ((35)10^4) + ((10)10^3) + ((5)10^2) + ((42)10^3) + ((12)10^2) + ((6)10^1) + ((21)10^2) + ((6)10^1) + ((3)10^0)

= ((350000) + (10000) + (500)) + ((42000) + (1200) + (60)) +( (2100) + (60) + (3))

= ((360500 + 43260) + (2163))

= (403760 + 2163)

= 405923

At first glance the formula seems very complicated but this is the best way I could figure out how to represent the number pattern. Once numbers become larger and more complex using rounding techniques to make mental math easier actually makes it harder and this pattern simplifies even the more complex multiplications. To simplify: The main difference between normal long multiplication and this formula is the direction in which you multiply (left to right versus right to left).

Once the pattern is understood all that is left is picturing the changing numbers in your mind, and practice.

This is why God created calculators.

This