Learning how to multiply two or three-digit numbers with each other can seem like a daunting task, not only for kids but for adults too.
Some are able to learn the principles quicker than others. Still, we all start from the same place – using written methods to understand the core principles. Only once we’ve mastered these can we go on to more difficult problems.
But what fundamental multiplication methods can help us on our journey? That’s what we’ll explore in this article.
We’ll take a look at the grid method, long multiplication method, column multiplication method, and how to multiply fractions. These methods will be the foundation upon which you can learn how to solve the most challenging multiplication questions.
Let's take a look at how to solve several multiplication problems.
How to do a multiplication with repeated addition
Repeated addition is one of the first ways to learn multiplication. As the name suggests, it involves using addition repeatedly to find the answer to a multiplication problem. This method has the benefit of teaching you the relationship between addition and multiplication, which is useful further in your education. Also, if your times tables knowledge isn’t fully formed yet, you’ll be to piece together simple addition.
Repeated addition example 1
Suppose we have to calculate the following problem: 3 × 3
Instead of learning the times tables, rearrange the question to 3 + 3 + 3 = 9.
It may seem simple, but this is repeated addition.
Repeated addition example 2
Suppose we have to calculate the following problem: 4 × 3
This question can be answered by rearranging it as 4 + 4 + 4 = 12 or 3 + 3 + 3 + 3 = 12. We reach the same answer but use a different equation.
How to do a multiplication grid
The multiplication grid method is a great way for young kids or adults to start learning multiplication skills. It makes everything simple and straightforward and helps you think about place value and multiples of ten and one hundred. This can accelerate learning as these are core principles when it comes to teaching multiplication.
The grid method involves separating numbers into tens and units in multiplication tables and then doing separate calculations. Breaking down each calculation step by step makes it easier to understand multiplication facts and also how they come together to produce the final answer. Let’s take a look at a few examples.
Grid method example 1 – one digit number multiplied by a two-digit number
Suppose we have to calculate the following problem: 18 × 5
First, we should know that the number 18 is made up of the tens’ 10’, and the units’ 8’.
We want to put this into a multiplication table that separates the tens and units of each number. It should look something like this:
| × | 10 | 8 |
| 5 |
You would then multiply the 5 × 10 = 50 and write the answer in the corresponding box, and multiply 5 × 8 = 40 and write the answer in the corresponding box. Your grid should now look like this:
| × | 10 | 8 |
| 5 | 50 | 40 |
All that remains is to add the two numbers together (50 + 40), which gives us a final answer of 90.
Grid method example 2 – two-digit number multiplied by a two-digit number
Suppose we have to calculate the following problem: 34 × 17
First, we should know that the number 34 is made up of the tens’ 30’, and the units’ 4’. We should also know that the number 17 is made up of the tens’ 10’ and the units’ 7’. We want to put this into a multiplication table that separates the tens and units of each number. It should look something like this:
| × | 30 | 4 |
| 10 | ||
| 7 |
You would then multiply the 10 × 30 = 300 and write the answer in the corresponding box. Then, multiply 10 × 4 = 40 and write the answer in the corresponding box. The next step is to do the same thing with the unit 7. So multiply 7 × 30 = 210 and write the answer in the corresponding box, and multiply 7 × 4 = 28 and write the answer in the corresponding box.
Your grid should now look like this:
| × | 30 | 4 |
| 10 | 300 | 40 |
| 7 | 210 | 28 |
All that remains is to add the answers together (300 + 40 + 210 + 28), which gives us a final answer of 578.
How to do long multiplication
The long multiplication method is an easy-to-remember method that is typically taught after the grid method. It is used to teach how to multiply a two-digit number with a three or more digit number. Due to its step-by-step nature, the long method can be applied to solve various multiplication calculations. Let’s dive straight into an example.
Long multiplication example 1
Suppose we have to calculate the following problem: 132 × 24
- Step 1: Write the largest number (132) at the top, with the smaller number (24) below it. Make sure you align the units with each other. You can then draw a horizontal line under the equation, as this is where your working out will be.
- Step 2: Multiply the two numbers in the ones column together. In this case, we multiply 4 × 2 = 8. Write 8 in the one’s column below the horizontal line.
- Step 3: Now, you want to multiply the 4 with the value in the tens column of the top number. In this case, we multiply 4 × 3 = 12. Write 2 in the tens column and add a small 1 above the top number on the hundreds column – this is what we’re carrying forward.
- Step 4: Now multiply the 4 with the 1, and then add the 1 we carried forward. This gives us a value of 5, which you can write in the hundreds column. This gives us a total answer of 528.
- Step 5: We want to repeat the same process with the tens column for 24, which we can write below the 528. In this case, we multiply 2 × 2 = 4. We can write the 4 below the 2 in the tens column and a 0 in the ones column, giving us an answer of 40.
- Step 6: Now multiply the 2 with the value in the tens column of the top number. In this case, we multiply 2 × 3 = 6. Write the 6 in the hundreds column. Since we are not carrying any numbers forward, we can move on to the next step.
- Step 7: Multiply the 2 with the value in the hundreds column of the top number. In this case, we multiply 2 × 1 = 2. Write 2 in the thousands column. This gives us a total answer of 2,640.
- Step 8: All that remains is to add the two answers together. 2,640 + 528 = 3,168.
These eight simple steps are all that it takes to solve multiplication problems using the long method. If you want to know how to multiply four-digit numbers instead of two or three, simply follow the same steps but with the additional numbers.
It can be a lot to remember at first, but if you take your time to understand each step, you’ll be able to take any two digits and multiply them together using this method.
How to do column multiplication
The column method is the exact same as the long multiplication method, just under a different name – often, people use the terms’ column method’ and ’long method’ interchangeably. Please refer back to the previous section to learn the column method.
How to do multiplication with fractions
Unlike adding or subtracting fractions, the denominator does not need to be the same for both fractions. However, it’s important to keep in mind that the fractions should be in proper or improper form, not mixed. As long as this holds true, you can multiply any fraction together using the following three multiplication steps:
- Multiply the numerators
- Multiply the denominators
- Simply the final answer to its lowest terms
Let’s take a look at this with a few multiplication questions with different examples.
Multiplying fractions example 1
Suppose we have to calculate the following problem: 1/4 × 4/5
- The first step is to multiply the numerators
This means we multiply 1 × 4 = 4
- The second step is to multiply the denominators
This means we multiply 4 × 5 = 20
- The final step is to simplify the final fraction to its lowest terms
4 is the greatest common factor in 4 and 20, which means we can divide both by 4 to simplify the fraction. 4 ÷ 4 = 1, and 20 ÷ 4 = 5. Therefore, our final answer is 1/5.
Multiplying fractions example 2 – same denominator
Now let’s take a look at how to multiply fractions with the same denominator. The rules don’t change, so we can follow the same three-step process as we did above.
Suppose we have to calculate the following problem: 1/5 × 3/8
- The first step is to multiply the numerators
This means we multiply 1 × 3 = 3
- The second step is to multiply the denominators
This means we multiply 3 × 8 = 24
- The final step is to simplify the final fraction to its lowest terms
3 is the greatest common factor in 3 and 24, which means we can divide both by 3 to simplify the fraction. 3 ÷ 3 = 1, and 24 ÷ 3 = 8. Therefore, our final answer is 1/8.
Multiplying fractions example 3 – different denominator
Now let’s take a look at how to multiply fractions with different denominators. As with the two examples above, the multiplication rules don’t change, so we can follow the same three-step process as we have previously.
Suppose we have to calculate the following problem: 3/9 × 6/10
- The first step is to multiply the numerators
This means we multiply 3 × 6 = 18
- The second step is to multiply the denominators
This means we multiply 9 × 10 = 90
- The final step is to simplify the final fraction to its lowest terms
18 is the greatest common factor in 18 and 90, which means we can divide both by 18 to simplify the fraction. 18 ÷ 18 = 1, and 90 ÷ 18 = 5. Therefore, our final answer is 1/5.
