Quickly Calculating the Product of Two 2-Digit Numbers

A resource about math tricks would not be complete without mention of the techniques of Vedic mathematics.  Vedic math was introduced by Bharati Krishna Tirthaji Maharaja in the first half of the 1900s, and are a collection of sutras which allow the user to quickly solve mathematical problems very efficiently.  Tirthaji claimed that these sutras were found while studying ancient Hindu writings, but confirmation of his explanation has never been made.

Vedic math can be used such that calculations can be performed mentally or very quickly using single-line notation.  This article will demonstrate the Vedic math technique of quickly calculating the product of two 2-digit numbers.

In this example, 32 will be multiplied by 43:

32
x43

First take the product of the right-most digits and multiply them.  Then, write the result under and to the right of the multiplication set:

32
  |
43
6

Next, take the product of each diagonal digits and add them together.  Write the sum to the left of the first result.  I will show this step in two parts:

32
 X
43
(3×3)+(4×2)   6

Which is the same as:
32
 X
43
17  6

Lastly, take the product of the left-most digits, and write the result to the left of the first two results:

32
 |
43
12  17  6

Almost done – now if you have any remainder in the tens columns, be sure to add it to the ones columns to the result to the left.  In our example, the “17” has a remainder of “1” in the tens columns, so add 1 to 12:

32
43
13  7  6

Now just “squeeze” the results together, and you will have your answer:

32
43
1376

And, indeed, if you use a calculator, you will find that 32 x 43 = 1376.

And now for a few more examples:

12×16:

12
16
1   2+6   12

12
16
1  8  12

192 answer

16×36:

16
36
3   24   36

16
36
3   24   36

16
36
3  27  6

16
36
5  7  6

576 answer

25×97:

25
97
18  45+14  35

25
97
18  59  35

25
97
18  62  5

25
97
24  2  5

2425 answer
Practice some more of your own on paper to get the technique down, and then try to do some in your head.  With a little practice, you will be able to do two-digit calculations quickly in your head!

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Dodecahedron Calendar

Happy New Year!  And with the new year, I have for you a neat little project that you can complete in a short time.  It is a 12 month dodecahedron calendar!  It is a perfect project that can be performed by students as an introduction to Platonic Solids, or by anybody who just wants a really cool calendar.  If you have very young children, I am sure they will find this a fascinating object – our two oldest boys (5 and 3) really enjoyed it, and now they can say “dodecahedron”!

Simply print the dodecahedron net below, cut it out on the black lines, fold the grey lines, and tape in the tabs such that the dodecahedron is formed.

To print the dodecahedron, click on the image to get the larger file in your browser.  You can then right-click the file to save it to your computer, or print it directly.

Click on the image to open the larger file.

A bit of patience is required when assembling the calendar, but I think you will be pleased with the results if you stick with it.  Below are some pictures I took while assembling one.  I used scissors to cut the dodecahedron, and they worked well enough.  If you have an x-acto knife, I would suggest using that instead.

Here is the dodecahedron net cut out and ready to be assembled:

Taping the tabs in:

More folding and taping:

More folding and taping:

Slow and steady, carefully folding and taping.  Did I mention that patience is required? Almost done:

Smoothing out the faces with a chop stick:

The finished product:

Our two oldest kids, stunned with the awesomeness of the dodecahedron calendar:

Again, just a bit of patience, and you will have a great calendar in the form of my favorite Platonic Solid.  I got a good result on my first attempt.  With a little practice, I am sure I can get better results in a shorted time – and so can you!

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The Four Fours

Here is an interesting math puzzle that you can play just about anywhere.  All you really need is paper and a writing instrument.  A calculator is not needed, but it is highly recommended!  The rules of this puzzle are simple enough, although there are some variants.  The rules given here are the ones I was given when I first learned of this math puzzle.

Using four fours, you are to find a mathematical expression for every whole number you can starting with zero.  You can use addition, subtraction, multiplication, division, factorials, decimal points, exponents, 0.4bar (i.e., the recurring decimal 0.44444. . .), and square roots.  Use of parentheses to emphasize the order of operations is not only allowed, but encouraged!

Some examples are:

0 = (4 + 4) – (4 + 4)

17 = (4 x 4) + (4 ÷ 4)

The Four Fours puzzle (a.k.a., The Four Fours Problem) has been known for years, and was described by Walter William Rouse Ball in his publication “Mathematical Recreations and Essays”:

Often times, there are multiple possible solutions.  How many can you find?

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Platonic Solid Christmas Ornaments

It’s that time of the year again, and this Christmas season we have something special for you – Platonic Solid Christmas Ornaments!  These Platonic Solid nets are ready for you to print out and fold into the coolest math Christmas ornaments on the planet!  Simply cut out the pattern, and fold along the grey lines.  Fold the tabs into the solids and adhere with double-stick tape or glue.  Alternatively, you can simple tape the sides together with regular tape.  After you get the solid constructed, attach some string and add it to your tree.  Santa will be so impressed, he will surely leave extra presents for you!

These polyhedron nets make great Christmas math activities for kids!  If you are a teacher, this will be a good basis for introducing your students to polyhedra – in this case the five regular polyhedra (the Platonic Solids).  All five Platonic solids are here in their Christmas costumes: tetrahedron, hexadedron, octahedron, dodecahedron, and the icosahedron.  If you want some material for your lesson plan, here is the link to the Platonic Solids at Wikipedia.

All files are in .PNG format (Portable Network Graphic).  Simply click on the image you desire to get the full size, and then right-click on it to get the “save as” option (or print it while viewing the full sized graphic).

These are the first in this series, but more will be added later.  Check back to see when more are added, or if you are on Facebook, you can get updates there – just visit our Facebook page and “Like” us!

 Green Tetrahedron Polyhedron Net

Red Tetrahedron Polyhedron Net

Santa Tetrahedron Polyhedron Net

Baby Jesus Tetrahedron Polyhedron Net

Poinsettias Tetrahedron Polyhedron Net

Snowflakes Tetrahedron Polyhedron Net

Candy Canes Tetrahedron Polyhedron Net

Christmas Motif Tetrahedron Polyhedron Net

Santa Shadow Tetrahedron Polyhedron Net

 Green Hexahedron Polyhedron Net

Red Hexahedron Polyhedron Net

Santa Hexahedron Polyhedron Net

Baby Jesus Hexahedron Polyhedron Net

Nativity Hexahedron Polyhedron Net

Merry Christmas Hexahedron Polyhedron Net

Christmas Bear Hexahedron Polyhedron Net

Poinsettias Hexahedron Polyhedron Net

Snowflakes Hexahedron Polyhedron Net

Candy Canes Hexahedron Polyhedron Net

Christmas Motif Hexahedron Polyhedron Net

Santa Shadow Hexahedron Polyhedron Net

Green Octahedron Polyhedron Net

Red Octahedron Polyhedron Net

Santa Octahedron Polyhedron Net

Baby Jesus Octahedron Polyhedron Net

Poinsettias Octahedron Polyhedron Net

 Snowflakes Octahedron Polyhedron Net

Candy Canes Octahedron Polyhedron Net

Christmas Motif Octahedron Polyhedron Net

Santa Shadow Octahedron Polyhedron Net

 Green Dodecahedron Polyhedron Net

Red Dodecahedron Polyhedron Net

Santa Dodecahedron Polyhedron Net

Baby Jesus Dodecahedron Polyhedron Net

Nativity Dodecahedron Polyhedron Net

Christmas Bear Dodecahedron Polyhedron Net

Poinsettias Dodecahedron Polyhedron Net

Snowflakes Dodecahedron Polyhedron Net

Candy Canes Dodecahedron Polyhedron Net

Christmas Motif Dodecahedron Polyhedron Net

Santa Shadow Dodecahedron Polyhedron Net

Green Icosahedron Polyhedron Net

Red Icosahedron Polyhedron Net

Santa Icosahedron Polyhedron Net

Baby Jesus Icosahedron Polyhedron Net

Poinsettias Icosahedron Polyhedron Net

Snowflakes Icosahedron Polyhedron Net

Candy Canes Icosahedron Polyhedron Net

Christmas Motif Icosahedron Polyhedron Net

Santa Shadow Icosahedron Polyhedron Net

 Happy Holidays from Math Tricks!

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