Multiplication is a way of adding a number to itself multiple times. It's a faster way to do repeated addition. When we multiply two numbers, we're finding the total amount when we have a certain number of equal groups.
Multiplying whole numbers starts with a solid knowledge of the multiplication table. The more you know your multiplication table, the easier it will be for you to perform multiplication of any size!
Here's why multiplication tables are so important:
Factors: The numbers being multiplied together
Multiplicand: The number being multiplied (the number in each group)
Multiplier: The number of groups
Product: The result of the multiplication
For example, in the multiplication 5 × 3 = 15:
In 8 × 6 = 48, which number is the product, and which is the multiplier?
48 is the product and 6 is the multiplier. There are 6 groups of 8, and the result is 48.
The easiest multiplication we can perform is with single digits because all we need is a good remembrance of the multiplication table. This we can see in the examples below.
| 4 | ||
| × | 3 | |
| 1 | 2 |
| 6 | ||
| × | 5 | |
| 3 | 0 |
| 7 | ||
| × | 4 | |
| 2 | 8 |
| 9 | ||
| × | 6 | |
| 5 | 4 |
Example: 231 × 2
| 2 | 3 | 1 | |
| × | 2 | ||
| 4 | 6 | 2 |
Steps:
2 × 1 = 2
2 × 3 = 6
2 × 2 = 4
Multiplying a three-digit number by a one-digit number may be a little bit more fun when there is regrouping. The following is a multiplication of a three-digit number by a one-digit number (247 × 3) with regrouping.
Please study this example carefully since other examples will build on this one!
Before we set up our multiplication vertically, let's understand what happens when we need to regroup (carry) numbers. We'll break down the process using 247 × 3 as an example.
Final Result: 741
Now we can set this up vertically to make it easier to solve! You can set it up vertically and get the same answer faster with less writing.
Example: 247 × 3
| 1 | 2 | ||
| 2 | 4 | 7 | |
| × | 3 | ||
| 7 | 4 | 1 |
Steps:
3 × 7 = 21; Write 1, carry 2
3 × 4 = 12, plus carried 2 = 14; Write 4, carry 1
3 × 2 = 6, plus carried 1 = 7
Multiply first, then add the carried digit. In 247 × 3, the tens step is 3 × 4 + 2 = 14. Adding the carry first, 3 × (4 + 2) = 18, gives a wrong answer.
Multiply 128 × 4 in columns.
512. 4 × 8 = 32: write 2, carry 3. 4 × 2 + 3 = 11: write 1, carry 1. 4 × 1 + 1 = 5.
Example: 456 × 27
First Partial Product (× 7)
| 3 | 4 | |||
| 4 | 5 | 6 | ||
| × | 7 | |||
| 3 | 1 | 9 | 2 |
Steps:
7 × 6 = 42: Write 2, carry 4
7 × 5 = 35, plus carried 4 = 39: Write 9, carry 3
7 × 4 = 28, plus carried 3 = 31: Write 1, carry 3
Write the carried 3
Second Partial Product (× 20)
| 1 | 1 | |||
| 4 | 5 | 6 | ||
| × | 2 | 0 | ||
| 9 | 1 | 2 | 0 |
Steps:
2 × 6 = 12: Write 2, carry 1
2 × 5 = 10, plus carried 1 = 11: Write 1, carry 1
2 × 4 = 8, plus carried 1 = 9: Write 9
Add a final 0 because we're actually multiplying by 20, not 2. In other words, since we are multiplying by 20, the digit in the ones place does not exist. But we can put a 0 as a placeholder.
Final Addition
| 1 | 1 | ||||
| 3 | 1 | 9 | 2 | ||
| + | 9 | 1 | 2 | 0 | |
| 1 | 2 | 3 | 1 | 2 |
Steps:
2 + 0 = 2
9 + 2 = 11: Write 1, carry 1
1 + 1 + 1 = 3
3 + 9 = 12: Write 2, carry 1
Write the carried 1
Key Points:
Don't forget the 0 placeholder in the second partial product. Without it, 456 × 27 would become 3,192 + 912 = 4,104, which is far too small.
Multiply 34 × 12 using partial products.
408. 34 × 2 = 68. 34 × 10 = 340 (write the 0 placeholder, then 34 × 1). 68 + 340 = 408.
Problem 1 guides you through every step of a three-digit by one-digit multiplication. Problem 2 multiplies two two-digit numbers in fewer, bigger steps, with a hint for each one. Problem 3 has no step-by-step help: you fill in the whole multiplication yourself, with one hint if you need it. You type every digit straight into the grid. You can skip a problem at any time, and each time you play you get new problems.
Practice Complete!
Type a number with up to 4 digits and a multiplier with up to 3 digits, then make your grid. Fill in the partial products and the answer, and check your work as often as you like. The “Carries” lines are there to help you; you don't have to fill them in.
The label on the left of each line of boxes says what goes in it. There is one line of carries and one partial product for each digit of the multiplier.