Example 1:

Multiply 432 by 8.

Solution:

       432

×        8

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      3,456

In multiplying the multiplier in the units column to the multiplicand, 8 x 2 = 16.  A 6 is placed under the units column, and 1 ten is carried.  After that, 8 x 3 = 24, plus the 1 carried over equals 25.

A 5 is placed under the tens column, and 2 hundreds are carried over.  Further, 8 x 4 = 32, plus 2 carried over, equals 34.  A 4 is placed under a hundreds column and a 3 under the thousands column.

Example 2:

What is the product of 176 x 59?

Solution:

  176

  x59

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1584  Multiplication by 9

880    Multiplication by 50

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10384

Start through multiplying the digit in the units place of the multiplier, 9 x 6 = 54.   Where A 4 is placed under the units column, or 5 tens are carried over.

In addition, 9 x 7 = 63, plus the 5 carried over which is equals 68.   An 8 is placed under the tens column, and 6 hundreds are carried over.  After that, 9 x 1 = 9, plus 6 carried over, equals 15. Where A 5 is placed under the hundreds column and a 1 under the thousands column.

The digit in the tens place of the multiplier is multiplied now: 5 x 6 = 30.  Because the 5 in 59 is in the tens column, a zero is placed under the tens column, and 3 tens are carried over.  Further, 5 x 7 = 35, plus the 3 carried over, equals 38.  Since 8 is placed under the hundreds column, & 3 hundreds are carried over.

Then, 5 x 1 = 5, plus 3 carried over which is equals 8. An 8 is placed under the thousands column. The results of 176 multiplied through 9 and 50 are then added to provide the final product.