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SAT Mathematics Level 2: Help and Review22 chapters | 224 lessons
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Free 5-day trialMia has taught math and science and has a Master's Degree in Secondary Teaching.
Teachers often have the challenge of instructing students that have different learning styles and abilities. For this reason, they need to offer them more than one strategy for solving a problem. Some students prefer a systematic process, while others prefer to use visual aids. It is also important for students to understand why a process works, rather than simply to follow the steps that a teacher shows them. In this lesson, we will discuss three methods for double-digit multiplication. They are the box method, distribution method, and column method; after which you can decide which one you prefer to use.
While the column method is the most commonly used strategy for multiplication, the box method is useful for understanding why the column method works. For this reason, we will look at the box method first and illustrate it with an example.
Find the product of 34 and 12.
The first step in the box method is to write each number in an expanded form, which is a way of writing numbers that shows the value of its digits. For example, in the number 34, the three is in the tens place so it is written as three tens, or 30. The four is written in the ones place so it has a value of four ones, or 4. In expanded form, we show 34 as 30 + 4 and 12 is 10 + 2.
Once we've written a number in expanded form, we can enter them into the table. To fill in the remaining spaces in the table, we multiply the numbers that represent the row and column for each box.
30 | 4 | |
10 | 300 | 40 |
2 | 60 | 8 |
The final step is to add the numbers in the boxes together, giving us 408.
300 + 40 + 60 + 8 = 408
Therefore, product of 34 and 12 is 408.
Let's look at another example while we are discussing the distribution method.
Find the product of 45 and 27.
The distribution method uses a similar strategy as the box method, but without having to draw the boxes. Instead the numbers are written in expanded form, and then placed in parentheses.
Next the distributive property is used to multiply the numbers. The distributive property tells us to multiply each number in the first set of parentheses by each number in the second set of parentheses. Lastly, we add the numbers together to get the product.
The column method is the most common way of multiplying double-digit numbers. Once it is mastered, it is faster and more efficient than the box or distribution methods. When using the column method, line up the numbers in the ones and tens places. Let's see how the column method would have worked for our first example.
Find the product of 34 and 12.
We begin by multiplying the first number, 34 by the digit in the ones place of the second number, which is two. This gives us 68
Next, we multiply 34 by the number in the tens place, which is one. This gives us 34. Since the one is in the tens place, it has a value of ten. To make sure that this is taken into consideration, we leave a space in the ones place when we multiply the 34 times one.
Just like the box and distribution methods, our last step is to add the numbers together.
In this lesson, we reviewed three methods for double-digit multiplication. All three methods use multiplication and addition to find the final product. In the box and distribution methods, write each number in expanded form first. The box method organizes the expanded numbers in a table format, while the distributive method uses parentheses. The column method is the most common method for multiplying double-digit numbers and does not require expanding the numbers. Instead, the numbers are arranged so that each ones and tens digits of each number are aligned vertically, and the digits can be multiplied in a systematic way.
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SAT Mathematics Level 2: Help and Review22 chapters | 224 lessons