Long arithmetic operations Multiplication

Multiplication combines several quantities into a single value, called the product. Multiplication means that the product of x and y is the result of x added together y times.

Long multiplication is a specific way of multiplying large numbers with more than two digits.

In the long multiplication method, the number on the top is called the multiplicand. The number by which it is multiplied (the number at the bottom) is called the multiplier.

How to do the long multiplication:

• Step 1: Put the numbers into a column based on their place value. Write the larger number on the top.
• Step 2: Multiply ones digit of the top number by the ones digit of the bottom number. Then, multiply the tens digit of the top number by the ones digit of the bottom number.
• Step 3: Place a 0 below the ones digit. Multiply the ones digit of the top number by the tens digit of the bottom number. Then, multiply the tens digit of the top number by the tens digit of the bottom number.
• Step 4: To obtain the results, add the two partial products.

Example:

Solve 89 x 75.

Solution:

Step1:

Multiply 5 by 9. Place 5 in the result line and carry 4. There’s one result line for each digit in 75.

Step2:

Multiply 5 by 8 and add 4. Place 4 in the result line and carry 4.

Step3:

Multiply 7 by 9. Place 3 in the result line and carry 6.

Step4:

Add the numbers in each column (4 + 2) and place 6 in the result line.

Step5:

Add the numbers in each column (0 + 6) and place 6 in the result line.

Answer: 6675