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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Katie Wimberley*

Expanded notation allows you to create simpler multiplication problems and add them together by breaking down one of the factors into smaller numbers. In this video, you'll learn how to use expanded notation and organize the information through the box method.

Have you ever taken one look at a multiplication problem and thought, ''Oh no! That's a huge number! I can't possibly multiply a number that big''? Fortunately, numbers can be broken down into smaller, less scary numbers, and then multiplied. This process is called expanded notation. **Expanded notation for multiplication** is similar to expanded form when working with place value. The number 62 **decomposes**, or breaks down, into 60 and 2. If we want to multiply 62 x 4, we can use expanded notation for multiplication. We would still expand 62 into 60 and 2, but we'd then multiply 60 x 4 and 2 x 4.

The **box method** is a way to organize the numbers used when solving with expanded notation for multiplication. Since we're completing a problem with a two-digit factor multiplied by a one-digit factor, we'll draw one row with two boxes in the row.

Above the two boxes we'll write the value of each digit in the two-digit number. In this example, we'll write 60 above one box and 2 above the other box. We'll then write the other factor on the side of the boxes; in this case, 4. We can also place the *x* symbol at the corner of the box to remind ourselves that we need to multiply.

When we multiply 60 x 4, we get the product 240. Even though 60 is a two-digit number, it's easy to use when multiplying. Since we know that 6 x 4 = 24, we can use our knowledge of place value to understand that 60 x 4 = 240, because the 6 in 60 is in the tens place; therefore, our answer must be 10 times more than 6 x 4. We'll write this number in the box under the 60. Since 240 is part of our product, but not the complete product for 62 x 4, it's called a **partial product**. Now, we'll multiply 2 x 4, which gives us 8. We'll write this second partial product in the box underneath the 2. Lastly, we'll add the partial products together: 240 + 8 = 248. The order in which we multiply doesn't matter because we're adding both partial products together for a final answer.

We can complete the same problem, 62 x 4, through expanded notation for multiplication without using the box method. For instance, we could write out each multiplication sentence and add our partial products together.

Let's look at another example for expanded notation for multiplication. Given the problem 79 x 6, we would first decompose 79 into 70 and 9. We would then multiply each of these numbers by 6, and add our partial products together.

**Expanded notation for multiplication** sounds like a long, complicated process, but it's really quite simple. It involves breaking down, or decomposing, a large number into two smaller numbers that can easily be multiplied by a single digit. The **box method** is a way to organize the numbers used when solving with expanded notation for multiplication. Just decompose the two-digit number into the value of its tens place and ones place, and then multiply each number by the other factor. There's no need to remember to regroup numbers or the order in which they're multiplied, because you're adding both **partial products**, or the incomplete products, together to get the final answer.

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Math for Kids23 chapters | 325 lessons

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