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SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

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Lesson Transcript

Instructor:
*Stephanie Matalone*

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will learn three different strategies for double digit multiplication including the traditional method, the box method, and the partial product method.

So, you know the basics of multiplication and how to find a product, a number that results from adding another number to itself a certain amount of times. You know that 4 times 3 is equal to 12 because you are adding 4 to itself three times.

You learned your multiplication tables and can do basic single multiplication but then the numbers got bigger, and now you are lost. What ever will you do? Don't worry, we will go over three methods to solve double digit multiplication problems: traditional, box and partial product.

The first method to solve double digit multiplication problems is called the **traditional method** in which the two numbers being multiplied are lined up on top of each other so that single digit multiplication can be used.

So let's say you need to multiply 12 by 32, you will follow these steps:

Step 1: Line up the two numbers being multiplied on top of one another. Ensure that the ones place, numbers further to the right, are on top of one another. Ensure that the tens place, numbers to the left of the ones place, are also on top of one another.

Step 2: Multiply the numbers in the ones place. In our example, 2 is multiplied by 2. The product, 4, is then placed right below the line in the ones place under both 2's.

Step 3: Multiply the bottom numbers' one place with the top numbers' tens place. In our example, the bottom 2 is multiplied with the top 1. The product 2, is then placed to the left of the 4 from Step 2.

Step 4: Put a zero in the ones place on the next line because we will now be multiplying a number from the tens place, rather than the ones place. Because of this, the product cannot be in the slot furthest to the right.

Step 5: Multiply the tens place on the bottom with the ones place on the top. In our example, 3 is multiplied by 2 to give 6, which is placed to the left of the 0.

Step 6: Multiply the tens place together. In our example, 3 is multiplied by 1 to give 3 which is placed to the left of the 6 in the bottom row.

Step 7: Add the two products together to get the final answer. In our example, 24 and 360 are added together to get the final answer of 384.

The next method that can be used to multiply double digit numbers is called the **box method** in which a grid is used to separate the tens and ones place to make multiplication easier. To multiply 12 and 32 using the box method, follow these steps:

Step 1: Draw a table with two rows and two columns. Place the two numbers being multiplied on the top and side of the box, splitting the numbers up by place over each row/column. Note that the number from the tens place must have a zero in the ones place. In our example, when 12 is broken up by place, we do not just simply place 1 and 2 over the columns (which would imply 1 + 2 = 3 when we want 12). We must place 10 and 2 over the columns (10 + 2 = 12).

Step 2: Fill in the table by multiplying the numbers from the corresponding row and column. To fill in the top left box, multiply 30 and 10 to get 300.

Step 3: Add all the numbers inside the table. In our example, add 300 + 60 + 20 + 4 to get the final answer of 384.

The last method for solving double digit multiplication is called the **partial product method** in which the two numbers are broken up like in the box method and their parts are multiplied together.

To solve 12 times 32 using the partial product method, follow these steps:

Step 1: Break up 12 and 32 into their tens and ones place like we did in the box method. Ensure that the number from the tens place has a placeholder of zero in the ones place.

Step 2: Multiply the number from the tens place in 12 by both numbers from 32. In our example, 10 is multiplied by both 30 and 2.

Step 3: Multiply the number from the ones place in 12 by both numbers from 32. In our example, 2 is multiplied by both 30 and 2.

Step 4: Add all the products together. In our example, 300, 20, 60, and 4 are all added together to give a final answer of 384.

In this lesson, we learned about three different methods to solve double digit multiplication problems. The first method was the **traditional method** where we lined up the two numbers and multiplied using the single digits from the bottom number. The second method, called the **box method** included setting up a table to split the numbers apart and multiplying the ones and tens places separately. The **partial product method** was the last one we went over, which involved splitting up the numbers and multiplying each place separately like the box method.

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SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

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