Methods for MultiplicationTutorial

By: Melinda Hallock

How to use this Tutorial Every slide has 3 pictures. Slide your mouse over each button to perform

a different operation.

Click this button on the bottom left of each slide to return to the

first slide.

Click this button on the bottom right of each slide to return to the previous slide.

Click this button on the bottom right of each slide to go to the next slide.

Introduction

Hopefully, you have a teacher who has taught you many ways to perform large digit multiplication. I want to show you some different ways and discuss which one I prefer and why. You can make up your mind about your favorite. I know there are many more methods than I will show you, but I will hopefully teach you something you didn’t know.

Standard AlgorithmThe standard algorithm in multiplication is the paper and pencil way that most people learned to multiply large

numbers in school. First you set up the numbers vertically and line the numbers in each place value up. 36

x 45Then you start with the bottom number in the ones place. You multiply it by the bop number in the ones place.

The answer to that number can be tricky. Take what is in the ones place and write it under the ones column. Take what is in the tens place and carry it above the 3 in the tens place.

Example: 336

x 45 0

Next multiply the bottom number in the ones place and add the number that you carried to the answer. Write the answer in tens and hundreds places under the line.

Example: 336

x 45 180

Now you are ready to multiply the bottom number in the tens place.

Standard Algorithm Cont….You need to put a 0 under the answer of what you just did. This is because you are multiplying 36 x 40 now and not 36 x 4, so you must save a space in the ones

place.Example:

36 x 45 180 0

No w you do the same thing you did before. Multiply the bottom tens place number by the top ones place. Write the number that is in the ones place now in the tens place beside your new 0 and carry what is in the tens place above the 3.

Example: 236 x 45 180 40

Next multiply the number in the bottom tens place by the top tens place and add what you carried. Write it in the hundreds and thousands place.Example: 2

36 x 45 180 14 40

Now add the 2 answers together and you have your answer.

Example 36 x 45 180 + 1440 1620

Standard Algorithm Thoughts

The standard algorithm doesn’t make sense at first. You need to practice it a lot and memorize the steps. Once you have it, it can be a lot of fun. A problem is that you need paper and pencil to do it, and you don’t always have those. Also, it takes time.

Using a CalculatorCalculators are simple to use when solving basic

multiplication problems.We will stick with our same problem: 36 x 45.Make sure your calculator has been cleared, so

press the clear button.Now press the numbers 36.Find the multiplication sign x and press it.Now type in 45.Press enter or =.The answer should appear on the screen. 1620

Click on the calculator above to use a calculator.

ThoughtsCalculators are easy to use. Most people always have one with them on their phones. They give you an accurate answer and fast.

Mental MathMental math is just that. You can do multiplication in your head. One problem can be done numerous ways. You manipulate the problem to use numbers that you

know and that are easy to you. Example: 36 x 45Round 36 up to 40. You have added 4.Round 45 up to 50. You have added 5.Multiply 40 x 50 =2,000. Since you added 4 and 5, you will need to take those away.So, multiply the 4 x 50=200. Take that away from 2,000. It leaves you with 1,800.Multiply the 5 x 40=200. Take that away from 1,800. It leaves you with 1,600.Now multiply what you added together. 4x5=20. Add that to 1,600, which give you 1,620.

You must find your own way to do it. Click here to view a forum.

Thoughts on Mental MathMental math can be done fast. It can also be done without pulling out any

paper or pencil. In a real-world situation, we will need to know how to do math quickly in our heads. People can make more mistakes when doing mental math. It’s hard to check over the work and see errors. Mental math users find a way for multiplication to make sense, so they are usually close to the answer.

Lattice MultiplicationLattice multiplication involves squares. Step 1: You multiply each number on the top outside of the squares to the numbers on the right

outside of the squares. The answer goes in the boxes where the two squares meet. The number in the tens place goes on the top half of the triangle. The number in the ones place goes on the bottom half of the triangle. Step 2: Do that for each number. If there is not a number in the tens place, then put a 0. Step 3: Add the numbers diagonally inside the boxes.

Step 3: Take those numbers and put them into place values. The 12 will change. The 1 will be added to the hundreds. So, you answer will be 1,620.

3 6

4

5

12

3 6

44

55

12

24

15

3

0

3 6

1

53

01

5

22

41

12 0

Step 1 Step 2 Step 3

Lattice Thoughts

Lattice multiplication is a fun way to multiply. It doesn’t make sense at first, and you must be taught the steps. I don’t think it’s an efficient way to multiply. It takes a long time and you must have paper and pencil. Unless, you have a lot of spare time, this is not the style for me.

SummaryAfter going through these methods, and thinking about them in debt, I have come to a conclusion about my

favorite, or should I say favorites. Mental math is a wonderful method. You can seem smart, and you don’t have to pull out any paper. It can be done fast the more you practice. There are also many times when you need to estimate and not find the exact answer. This is also a case where mental math would be the best method.

Another method in certain situations that would be best would be using a calculator. It’s fast and handy. If you carry a phone, more than likely you always have one at your fingertips. So, if you need an exact answer quickly, then use a calculator.