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Maths Tricks
Multiply Up to 20X20 In Your
Head
In just FIVE
minutes you should learn to quickly multiply up to 20x20 in your head. With this trick, you will be able to multiply any two numbers from 11
to 19 in your head quickly, without the use of a calculator.
I will assume that
you know your multiplication table reasonably well up to 10x10.
Try this:
·
Take 15 x 13 for an example.
·
Always place the larger number of the two on top in
your mind.
·
Then draw the shape of Africa mentally so it covers
the 15 and the 3 from the 13 below. Those covered numbers are all you need.
·
First add 15 + 3 = 18
·
Add a zero behind it (multiply by 10) to get 180.
·
Multiply the covered lower 3 x the single digit
above it the "5" (3x5= 15)
·
Add 180 + 15 = 195.
The 11 Rule
You likely all
know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you
know the 11 rule? It is as easy! You should be able to do this one in you head
for any two digit number. Practice it on paper first!
To multiply any
two digit number by 11:
·
For this example we will use 54.
·
Separate the two digits in you mind (5__4).
·
Notice the hole between them!
·
Add the 5 and the 4 together (5+4=9)
·
Put the resulting 9 in the hole 594. That's it! 11
x 54=594
The only thing
tricky to remember is that if the result of the addition is greater than 9, you
only put the "ones" digit in the hole and carry the "tens"
digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2
in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627
... 11 x 57 = 627
Square a 2 Digit Number Ending
in 5
For this example
we will use 25
·
Take the "tens" part of the number (the 2
and add 1)=3
·
Multiply the original "tens" part of the
number by the new number (2x3)
·
Take the result (2x3=6) and put 25 behind it.
Result the answer 625.
Try a few more 75 squared ... = 7x8=56 ... put 25
behind it is 5625.
55 squared = 5x6=30 ... put 25 behind it ... is 3025. Another easy one!
Practice it on paper first!
Squaring Two-Digit Numbers Quickly
First, determine the closest number to your number that ends in a
zero. In this example, the number is 20.
Next, determine the difference between your number and the closest number
with the zero. In this case, it will be (23 – 20) = 3.
Add the result to your number (23 + 3 = 26). Now, multiply the number
with the zero by the sum of your number and the difference you determined:
20 x 26 = 520
Now square the difference you determined before, and add it to the result
above:
(3 x 3) + 520 = 529
The Square of 25
Closest zero number: 20 (note – 30 will also work in this example)
Difference: 25 – 20 = 5
Sum: 25 + 5 = 30
Answer: (5 x 5) + (20 x 30) = 25 + 600 = 625
The Square of 37
Closest zero number: 40
Difference: 37 – 40 = -3
Sum: 37 + -3 = 34
Answer: (-3 x -3) + (40 x 34) = 9 + 1360 = 1369
The Square of 81
Closest zero number: 80
Difference: 81 – 80 = 1
Sum: 81 + 1 = 82
Answer: (1 x 1) + (80 x 82) = 1 + 6400 + 160 = 6561
Noticed how I broke down the (80 x 82) into (80 x 80) + (2 x 80)!
The Square of 12
Closest zero number: 10
Difference: 12 – 10 = 2
Sum: 12 + 2 = 14
Answer: (2 x 2) + (14 x 10) = 4 + 140 = 144
Multiply By 4
To quickly
multiply by four, double the number and then double it again.
Often this can be
done in your head.
Multiply By 5
To quickly
multiply by 5, divide the number in two and then multiply it by 10. Often
this can be done quickly in your head.
The 11 Rule Expanded
You can directly
write down the answer to any number multiplied by 11.
·
Take for example the number 51236 X 11.
·
First, write down the number with a zero in front
of it.
051236
The zero is
necessary so that the rules are simpler.
·
Draw a line under the number.
·
Bear with me on this one. It is simple if you work
through it slowly. To do this, all you have to do this is "Add the
neighbour". Look at the 6 in the "units" position of the number.
Since there is no number to the right of it, you can't add to its
"neighbour" so just write down 6 below the 6 in the units col.
·
For the "tens" place, add the 3 to the
its "neighbour" (the 6). Write the answer: 9 below the 3.
·
For the "hundreds" place, add the 2 to
the its "neighbour" (the 3). Write the answer: 5 below the 2.
·
For the "thousands" place, add the 1 to
the its "neighbour" (the 2). Write the answer: 3 below the 1.
·
For the "ten-thousands" place, add the 5
to the its "neighbour" (the 1). Write the answer: 6 below the 5.
·
For the "hundred-thousands" place, add
the 0 to the its "neighbour" (the 5). Write the answer: 5 below the
0.
That's it ... 11 X 051236 = 563596