Mathematical problems can be solved in multiple ways. In order to develop strong mathematical acumen, I advice my students to practice as many approaches as they can think of and then finally suggest the ones that best fit the specific case. For example, there are many ways to solve a two digit multiplication question.

Let's look at this one:

Let's look at this one:

**54 * 56****Condition**

- Digit at "Tens" place, T1 and T2, is same for both the numbers
- Sum of digit is "Units" place, U1 and U2 is 10

In this example, both T1 and T2 are 5; and sum of U1 and U2 is 4+6 which is 10

In this example, both T1 and T2 are 5; and sum of U1 and U2 is 4+6 which is 10

**Magic**

Step 1: Multiply the digits at "Units" place, U1 * U2

Step 2: Multiply the digit at "Tens" place, T1 to one number more than it, (T1 + 1)

Step 3: Add "output from Step 1" on right of "output from Step 2"

In the example above, output of Step 1 is 5 * (5+1) = 30; output from step 2 is 4 * 6 = 24; and the answer is

**3024.**

**Reason**

Let T1U1 and T2U2 be the two numbers.

*Given*

U1 + U2 = 10 ...(1)

T1 = T2 = T ...(2)

T1U1 = T1*10 + U1

T2U2 = T2*10 + U2

T1U1 * T2U2 = T * U2 * 10 + T^2 * 100 + T * U1 * 10 + U1 * U2

U1 + U2 = 10

T * U2 * 10 + T * U1 * 10 = T * (U1 + U2) * 10 = T * 100

T^2 + T * 100 + U1 * U2 = T(T + 1)* 100 + U1 * U2

T1U1 * T2U2 = T(T + 1) U1 * U2, where U1 * U2 forms the last two digits of the product, and T(T + 1) forms the first digits of the answer.

Introducing these tricks will make math interesting and fun. This generates curiosity to know why and how these tricks work and the exploration begins.