Multiply

Multiplication is one of the four basic operations in elementary arithmetic and can be considered repeated addition. It's the mathematical operation of scaling one number by another number. If you want to know how to multiply by the addition or the long multiplication method, just follow these steps.

Steps

Use Addition

  1. Write down the problem. You are solving the problem 4 x 3. This is really another way to say "3 groups of four."
    • You can think of this as repeated addition, where the number four will be repeated 3 times. But you are adding the number the amount of times you want to multiply it by.
  2. Solve through repeated addition. Knowing that each of the four groups have three objects, add 4 three times. 4 + 4 + 4 = 12
    • You can also find 4 groups of 3 instead. This will give you the same answer. Just add up the numbers in the problem 3 + 3 + 3 + 3 and you will get 12, the same answer.

Use Long Multiplication

  1. Line up the numbers you are multiplying. Place the larger number on top of the smaller number and line up the units in the hundred's, tens', and ones' place. In the problem 187 * 54, you should line up 7 over 4, 8 over 5, and 1 over no number, since 54 has no number in the hundred's place.
    • Write the multiplication sign below the top number and draw a line below the bottom number. You will start multiplying the numbers below the bottom line.
  2. Multiply the number in the ones' place of the bottom number with the number in the ones' place of the top number. Multiply 4 * 7. Your answer is 28, so write the number 8 from the number 28 below the 4, and carry the 2 from the number 28 over on top of the 8.
    • Any time your answer is two digits long, carry the first digit above the number next to the top first right number, and place the second directly below the number on the second row you were using to multiply.
  3. Multiply the number in the ones' place of the bottom number with the number in the tens' place of the top number. First, you multiplied 4 by the number in the ones' place; now, multiply it by the number in the tenths place. Multiply 4 with 8, the digit to the left of 7. 8 x 4 = 32. Remember that you had placed a 2 over the 8. Now, add it to your answer. 32 + 2 = 34.
    • Place the 4 from the number 34 below the line under the 8, next to the number 8 that you wrote down in the previous step.
    • Carry the 3 from the number 34 over the 1 in the number 187.
  4. Multiply the number in the ones' place of the bottom number with the number in the hundreds's place of the top number. You just multiplied 4 by the number in the tenths' place; now, multiply it by the number in the hundred's place. 4 x 1 = 4. Now, add the number that you carried above one to your answer. 3 + 4 = 7. Write this number down on the line below the one.
    • You have used long multiplication to multiply 4 by 187 to get 748.
    • Note that if the top number had four or more digits, you would just repeat the process until you multiplied the number in the ones' place of the bottom number with all of the numbers in the top number, continuing to move from right to left.
  5. Place a zero in the ones' place below your new product. Place a zero in the ones' place of the new row below the 8 in 748. This is just a placeholder for this method to show that you are moving on to multiply the tenths' place value.
  6. Multiply the number in the tenths' place of the bottom number with the number in the ones' place of the first number. Multiply 5 times 7 to get 35.
    • Write down the 5 from 35 to the left of the 0 and carry the 3 from the 35 above the 8 in the top number.
  7. Multiply the number in the tenths' place of the bottom number with the number in the tens' place of the first number. Multiply 5 by 8 to get 40. Add the 3 above the 8 to 40 to get 43.
    • Write down the 3 from 43 to the left of the 5, and carry the 4 from the 43 above the 1 in the top number.
  8. Multiply the number in the tenths' place of the bottom number with the number in the hundred's place of the first number. Now, multiply 5 times 1 to get 5. Add the 4 over the 1 to 5 to get 9. Write it down next to the 3.
    • You have done long multiplication to multiply 5 by 187. Your answer for that portion is 9350, since the 5 was in the tens' place.
  9. Add the top and bottom products. Just do simple addition to add your two products, 748 and 9350, and you're done.
    • 748 + 9350 = 10098



Tips

  • Remember anything multiplied by zero is zero!
  • To multiply by 10, add a zero to the end.
  • If you have a three digit number for the second row, you will need two placeholders to move on to multiplying the hundred's place value. For the thousand's place you will need three, so on and so forth.
  • It doesn't matter which number is on the top and which number is on the bottom.

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