How to Multiply Integers: 11 Steps

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2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

Multiplication is one of the four basic operations of elementary arithmetic and can be considered a repeated addition. It is a mathematical operation in which one number is increased by another number. If you want to learn how to multiply by addition or using the long multiplication method, please follow the steps below.

Steps

Method 1 of 2: Using addition

Step 1. Write down the problem

You have to solve the "4 x 3" problem. This is another way of saying "3 groups of 4".

You can think of it as a repeated addition, where the four will be repeated 3 times

Step 2. Solve using repeated addition

Knowing that each of the four groups has three objects, add 4 three times. 4 + 4 + 4 = 12

You can also consider 4 groups of 3. This will give the same result. Simply add the numbers from the problem "3 + 3 + 3 + 3" and you get 12, the same result

Method 2 of 2: Using long multiplication

Step 1. Line up the numbers you are multiplying

Write the larger number on top of the smaller one and align the units with the hundreds, tens and units. In multiplication "187 * 54", you must align 7 above 4, 8 above 5 and 1 above no number, since 54 has no digits in the hundreds place.

Write the multiplication sign under the top number and draw a line under the bottom number. You will start multiplying the number below the bottom line

Step 2. Multiply the digit in the units place of the bottom number by the digit in the units place of the top number

Multiply 4 * 7. The result is 28, write the 8 of 28 under the 4, and write the 2 of 28 up above the 8.

Whenever a result has two digits, put the first digit above the digit next to the top right number, and put the second digit directly below the number in the second row you were using in multiplication

Step 3. Multiply the digit in the units place of the bottom number by the digit in the tens place of the top number

First, you multiplied 4 by the digit in units; now, multiply 4 by the digit in the tens. Multiply 4 by 8, the left digit of 7. 8 x 4 = 32. Remember that you added a 2 above the 8. Now, add it to the result. 32 + 2 = 34.

Put the 4 of 34 under the 8, next to the 8 you wrote in the previous step.
Write the 3 of 34 over the 1 of 187.

Step 4. Multiply the digit in the place of the units of the bottom number by the figure in the hundreds place of the top number

You just multiplied the tens figure; now multiply the number in the hundreds. 4 x 1 = 4. Now, add the number you wrote down on top of one. 3 + 4 = 7. Write this number in the line under the one.

You used long multiplication to multiply 4 by 187 to give 748.
Note that if the top number had four or more digits, you would have had to repeat the process until you multiplied the digit in the units place of the bottom number with all the digits of the top number, going from right to left.

Step 5. Put a zero in the place of the units in the new product

# Put a zero in the units 'place in the new row below the 8 of 748. This is just a placeholder to indicate that you are multiplying the value in the tens' place.

Step 6. Multiply the digit in the tens place of the bottom number by the digit in the units place of the first number

Multiply 5 by 7 to give 35.

Write 5 of 35 to the left of the 0 and move the 3 of 35 over the 8 of the top number

Step 7. Multiply the digit in the 10's place of the bottom number by the 10's place in the first number

Multiply 5 by 8 to give 40. Add the 3 above the 8 to 40 to give 43.

Write 3 of 43 to the left of the 5 and move the 4 of 43 over the 1 of the top number

Step 8. Multiply the digit in the tens place of the bottom number by the hundreds place in the first number

Now, multiply 5 by 1 to give 5. Add the 4 above the 1 to 5 to give 9. Write it next to the 3.

You used long multiplication to multiply 5 by 187. The result for that part is 9350

Step 9. Add the top and bottom products together

Do a simple addition to add the two products, 748 and 9350, and you're done.

748 + 9350 = 10098

Advice

It doesn't matter which number is above or below.
Remember that any number multiplied by zero is zero!
If you have a three-digit number in the second row, you will need two placeholders to proceed to multiply the digits in the place of the hundreds. For the place of thousands you will need three and so on.

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