Multiplying Two Digit Numbers

Category: Arithmetic

"Published in Suisun City, California, USA"

How do you multiply a two digit number with another two digit number without using a calculator in a shorter way and faster? I will show you a technique. Let's consider this one:

23 x 34

By usual method,
        1
        2  3
  x    3  4
 ---------------
    1   9  2
    6  9
 ---------------
    7  8  2

Now, let's consider the other method which is Mayan Method. In this method, you will use the straight lines and their points of intersection. 

For 23, draw 2 parallel lines and then another 3 parallel lines  that are all parallel to each other.

For 34, draw 3 parallel lines and then another 4 parallel lines that are parallel to each other.

Divide the figure into three sections. At each section, count the number of points which are the points of intersection.

Therefore, the answer is 782.

Cubing - Two Digit Number

Category: Arithmetic, Algebra

"Published in Suisun City, California, USA"

How do you cube a two digit number without using a calculator in a shorter way or faster? Is that possible? Yes, it is. I will show you the technique. Let's consider this one:

(23)³

By usual method,

           2 3
    x     2 3
  ---------------
        1  6 9
        4 6
  ---------------
            1
            2
        5 2 9
   x      2 3
  ---------------
     1 5 8 7
  1 0 5 8
  ---------------
  1 2 1 6 7

Now, let's consider the better way. Cube each digits first and write this way:

Next, we need the next two terms at the middle. Let's consider the next steps. 

Square the first digit and then multiply with the second digit and then multiply by 3. In this case, 3(2)²(3) = 36.

Square the second digit and then multiply with the first digit and then multiply by 3. In this case, 3(2)(3)² = 54.

Therefore, the answer is 12167.

Finding Unknown Coefficients - Quadratic Equation

Category: Algebra

"Published in Newark, California, USA"

Find the value of k to the given equation

if one root is double the other.

Solution:

Consider the given equation

If a = 2, b = k, and c = 25, then substitute these values to the Sum of the Roots Formula

From the word problem, if r₁ = 2r₂, then

From the Product of the Roots Formula

Substitute the value of the variables to the above equation

Therefore, the answer is k = 15.