Lesson 3

Whole Number Multiplication

Introduction

Here you’ll learn how to multiply whole numbers.

Vocabulary

Here are the vocabulary words used with whole number multiplication.

Factor the numbers being multiplied in a multiplication problem

Product the answer to a multiplication problem

Multiplier the number you multiply with (also a factor)

Multiplicand the num ber being multiplied (also a factor)

alt

INFORMATION

A general concept overvew statement or word problem exercise can be placed in the concept introduction section.

Depending on the monitor size and orientation this page should be adjusted for optimal reading using Alt-U to select columns or scrolling and to adjust the text size.

Guidance

It is time to move forward and learn about multiplying whole numbers.

Addition and multiplication are related. Understanding that will help you understand what you doing when carrying out long-multiplication.

5 × 6 =  

You can easily use your times tables to complete this problem using mental arithmetic, but let’s try to understand what this problem of multiplying 5 and  6 actually means.

5 × 6 means that we can have five groups of six items. Here we have five groups of six different shapes. Count them and you will see there are 30 shapes.

▲▲▲▲▲▲ ■■■■■■ ◇◇◇◇◇◇ ●●●●●● ▼▼▼▼▼▼

So this is six added together five times. Think of it like this:

6 + 6 + 6 + 6 + 6 =

We can also think of this another way too. We could arrange it as six groups of  five shapes. There are still 30 shapes. You can count them if you want.

▲▲▲▲▲ ■■■■■ ◇◇◇◇◇ ●●●●● ♦♦♦♦♦ ▼▼▼▼▼
5 + 5 + 5 + 5 + 5 + 5 =

However all that horizontal addition is just too much work which is why we have the times-tables and why you learnt them in your early school years. We all know the answer to this.

5 × 6 = 30

So it would appear that multiplication is way to make really long addition problems short. And that is what it is and does.

The multiplication Vocabulary

5 and 6 are factors in this problem.

So what is a factor ?

A factor is the name give to  each of any two values being multiplied. In our example above 5 and 6 are factors.

When we multiply two factors together we get the product of those numbers. In our simple problem above the product of the factors 5 and 6 is 30.

That means the product is the answer to a multiplication problem.

Now let’s take what we have learned and look at how to apply it to a few more challenging problems.

Arranging Multiplication Vertically

Let's take a look at this problem:

567 × 3 =  

If you think about this like addition, it is 567 added three times. That is a lot of work, so we use our long multiplication short cut and rearrange it vertically taking care to get our place values correct.

  H T U
  5 6 7
  ×   3
       

 When we arrange our problem vertically we also get two new vocabulary terms based on the way we organize the problem. Look at this:

Multiplicand
× Multiplier
Product

 The top row is the biggest number and is called the multiplicand or the number being multiplied.

The middle row is usually the smaller number and is called the multiplier or, the number doing the multiplying.

The result of the problem is the product as we have already learnt.  Now let us see this in action!

Guided Tutorial 1. Vertical-Multiplication

This guided practice will show you how to set up your multiplication problem and use your simple times table knowledge to get the correct answer.

 Step 1. Place Values

  H T U
  5 6 7
  ×   3
       

We are now going to multiply 567 by 3.

First set the sum up vertically in their correct place values.

The big number on the top multiplicand and the smaller number on the bottom is the multiplier.

Both can also be called factors.

 Step 2 Multiply the Units

    2  
  5 6 7
  ×   3
      1

The multiplicand 567 is multiplied by the first multiplier digit which is 3.

When we multiply 7 by 3, we get 21. So 1 is placed in the product line.

We carry the 2 forward to the Tens column.

 Step 3 Multiply the Tens

  2 2  
  5 6 7
  ×   3
    0 1

Now we are now going to multiply 6 by 3.

We get the result 18.

Now must remember to add the 2 which we carried forward. The result is 20.

So 0 is placed in the product line and we carried the 2 forward to the Hundreds column.

 Step 4 Multiply the Hundreds

1 2 2  
  5 6 7
  ×   3
  7 0 1

Now we multiply 5 x 3 and the answer is 15.

Now add the 2 in the Hundreds column which we carried forword. The result is 17.

The 7 is placed in the product line.

The 1 is  carried forward to the Thousands column.

 Step 5. Multiply the Thousands

1 2 2  
  5 6 7
  ×   3
1 7 0 1

There are no more numbers in the multiplicand.

The 1 in the Thousands column can be put into the product line in the Thousands place value.

 Step 6. The Answer

1 2 2  
  5 6 7
  ×   3
1 7 0 1

Here is our final result.

567 multiplied by 3 is equal to 1,701.

   

= END OF TUTORIAL =

◀ Slide for more ▶

alt

PRODUCTION NOTE

Sliding panel interactive tutorials have been set to 500px width. Their size cannot be changed. Make sure you Adjust your monitor/viewport appropriately (Alt-U). If you are using a desktop or projector two column view is recommended. Use full-screen (F-11). If you are on a mobile device, scrolling page portrait orientation is recommended.

Guided Tutorial 2. Long-Multiplication

That was pretty straight-forward. Now, what happens when there is more than one digital in the multiplier. We have to arrange our problem a little differently and introduce some addition.

2 3 4 × 1 2 =  

 Step 1. Place Values

  H T U
  2 3 4
  × 1 2
       
       
       
       

We are going to multiply 234 x 12. We set the sum up vertically.

The big number is the multiplicand and the smaller number is the multiplier.

This time we are leaving space between the multiplier and product lines as a calculation area. There needs to be a work-line for each digit in the multiplier.

 Step 2. Multiply the Units

       
  2 3 4
  × 1 2
       
  4 6 8
       
       

The multiplicand 234 is multiplied by the first digit which is 2.

As we multiply each number we place the result in the first workline in the calculation area.

The result is 468.

 Step 3. Multiply the Tens

  H T U
  2 3 4
  × 1 2
       
  4 6 8
      0
       

We are now going to multiply 234 by the 10's digit which is 1.

Before we start the multiplication we put a 0 in the next work-line to make the result a 10× multiplication.

This is very important to understand and remember.

 Step 4. Multiply the Tens... Continued

       
  2 3 4
  × 1 2
       
  4 6 8
2, 3 4 0
       

We multiply 234 by 1 and put the result 234 into the work-line before the 0.

 Step 5. Adding the Work Lines

       
  2 3 4
  × 1 2
  1    
  4 6 8
2 3 4 0
2 8 0 8

The last step is to add the work-line columns. This is standard long-addition.

There is a carry-line at the top of the work-lines to let us handle any carry values that may come up.

In this example a 1 was carried into the Hundreds column.

 Step 6. The Answer

       
  2 3 4
  × 1 2
  1    
  4 6 8
2 3 4 0
2 8 0 8

We now have our final answer. The product of 234 multiplied by 12 is 2,808.

Remember the multiplication vocabulary.

 

 

= END OF TUTORIAL =

 ◀ Slide for more ▶

Video Review

These videos will giv e you another view and help you with multiplying whole numbers.

  Take the time to complete all the Exercises and use the Practice and Test Interactive tools to make sure multiplication becomes your friend. Learn to enjoy the numbers. They are fun and these exercises let you do it all at your own speed anytime you want.

 

©2005-16 Infogrid Pacific Pte. Ltd, Singapore.