Math Trick — Multiply Two Digit Numbers

Multiply Two Digit Numbers
Most people pull out their calculators every time they are faced with a math problem, but this doesn’t have to be you. There are various math tricks that one can learn to help solve math problems more quickly and efficiently. Here a few tricks you can use to multiply two digit numbers as high as 19 x 19.

Trick #1: The Two-Step Method

This math trick is extremely fast and simple. In just two steps, you can multiply two digit numbers between 11 to 19.

Step #1: Multiply the ones digits in each factor together. Write down the answer and carry any numbers if necessary.

Step #2: Determine what ones digit is smaller between each factor. Use that number and add it to the whole number of the larger factor. If there are any carried numbers, add those as well. Write down those numbers next to your first number.

Voila! You have your solved equation. Let’s look at it with numbers.

Equation: 14 x 15

Step #1: Multiply 4 by 5, which equals 20. Write down the zero and carry the 2.

Step #2: Find the smaller ones digit in the factor, which is 4, and add that to the larger factor – 15. Add the 2 that you carried from the first step. This means your equation is 4+15+2 = 21. Add 21 next to zero.

Your final answer: 210.

Trick #2: The Cross-Multiply Trick

This math trick is still fast but requires a few additional steps. The key to this method is to set your equation up so each factor is sitting on top of one another.

Step #1: Multiply the ones digits together and write down your answer. Carry any products if necessary.

Step #2: Cross multiply and add the numbers together. If you had to carry a number from step one, make sure to include it in your addition. Carry any products again if needed.

Step #3: Multiply just the tens digits. If you carried a product from step #2, add that to your answer.

Step #4: Combine all your answers.

Let’s test it now.

Equation: 14 x 15

Step #1: Multiply 4 by 5, which equals 20. Write down the zero and carry the 2.

Step #2: Cross-multiply 5 by 1 and 4 by 1. You will need to add 2 to your answer from the 5×1 equation. This is because of the 2 you carried from step #1. Your equation should look like 7 + 4 = 11. Write the 1 and carry a 1.

Step #3: Multiply 1 by 1, which equals 1. You will then add the 1 from step #2. This means your answer is 2. Write it down.

Step #4: Combine your answers.

Your final answer: 210

Here is the same problem written out a different way:

Trick #3: Multiply By 11

If one of your factors is an 11, use this trick to make the process even faster. It takes just a few simple steps and you’ll have an answer in no time.

Step #1: Find the factor that is NOT 11. Separate each number with a space in between them.

Step #2: Using that same factor, add the tens and the ones digits together. Place the product in the blank space between the two digits in step #1.

And that’s your answer. Let’s try it with numbers. It may make a little more sense.

Equation: 14 x 11

Step #1: Determine what factor is not the 11. In this equation, it is the 14. Separate the digits so your answer looks like this: 1_4.

Step #2: Add the digits in the factor from step #1 together. This means 1 + 4 = 5. Put the 5 in the blank space in your answer.

Your final answer: 154

In step #2, if you add your numbers together and they are more than 10, you will need to carry the product and add it to your first digit. Let’s look at an example.

Equation: 19 x 11

Step #1: Find the factor which is NOT the 11. In this case, it is the 19. Separate the number with a space in between. Your answer should look like this: 1_9

Step #2: Add the digits in the factor together. This means add the 1 and the 9. This gives you 10. Write down the zero in the blank space. You need to carry the 1 and add that to your hundreds digit.

Your final answer: 209

With a little practice, you may eventually be able to multiply two digit numbers in your head.

Test your skills by playing a few Math quizzes on Sporcle.