How to Find the Product of A Math Problem

Finding Products with Multiplication

A product is the answer that you get when you multiply numbers together. For instance, the product of two and three is six, because 2 x 3 = 6. Multiplication is just a fancy way of adding several numbers together. A multiplication problem tells you that there are a certain number of sets containing a certain number of units, and you have to add the units in all of these sets together to find the product.

For example, in the problem 2 x 3, you have three sets of two. Since 2 + 2 + 2 = 6, then 2 x 3 = 6. Likewise, for the problem 6 x 4, there are four sets of six. If you add together all four sets (6 + 6 + 6 + 6), you'll get 24, which is the product of 6 x 4.

It helps to visualize this process with concrete objects. Imagine that three of your friends each gave you five pieces of candy. You would have 15 pieces, since 5 + 5 + 5 = 5 x 3 = 15.

Multi-digit Numbers

After you've learned to multiply two single-digit numbers together, you'll practice multiplying single-digit numbers by multi-digit numbers. For instance, you might multiply 3 x 27 or 6 x 2,097. To do this, follow the steps below:

1. Write the single-digit number underneath the digit in the ones place of the larger number, and draw a horizontal line below it.
2. Multiply the single-digit number by the number directly above it. Then, record the answer underneath the horizontal line, directly below the single-digit number. If the answer has two digits, write the digit in the ones place below the horizontal line and carry the number in the tens place.
3. Multiply the single-digit number by the digit in the tens place of the larger number. Record the digit in the ones place of the answer immediately to the left of the answer from the previous step, and carry the number in the tens place if necessary.
4. Repeat this process until you've multiplied the single-digit number by each digit in the larger number and recorded the answers below the horizontal line.

Double-digit Multiplication

In fourth grade, you'll be asked to multiply double-digit numbers, like 15 and 25. To find the product of two double-digit numbers, follow these steps:

1. Write one number directly above the other so that their digits are lined up. Then, draw a horizontal line underneath the bottom number.
2. Label the number in the top left corner 'A' and the number in the top right corner 'B.' The number in the bottom left position is 'C,' and the number in the bottom right position is 'D.'
3. Multiply the number labeled 'D' by each digit in the top number (digits A and B), just like you would if you were multiplying a single-digit number by a multi-digit number. Record your answers below the horizontal line.
4. Before moving onto the number labeled 'C', write a zero underneath the digit in the ones place underneath your first answer.
5. Multiply the number that's labeled 'C' by the digits in the top number (A and B). Follow the same process you did when you multiplied digit D by this number, but record your answers to the left of the zero.
6. Add together your two products to get the final answer.