Whole Numbers

Algorithms

Standard Addition Algorithm

Similar to the partial sums algorithm, except a person must begin with the right-hand column and proceed to the left one column at a time. The exchange is recorded at the top of the next column.

Lattice Addition Algorithm

This is basically the whole-group algorithm recorded in a different format.

Partial Sums Algorithm

One column is combined and exchanges completed before another column is added. With this algorithm it does not matter which column is completed first; i.e. the columns may be added in any order.

Expanded Notation Algorithm

Write the number in expanded notation and then perform the operations.

Whole-group Algorithm

The procedure is to add each column separately, then perform the necessary exchanges.

View the Addition of Whole Numbers

Practice

Algorithms

3+ Digits by 2-Digit

102 x 58= ?
Rewrite the problem vertically.
Multiply 102 by 8. Write the product (816).
Place a 0, as a place holder, below the product of 816 in the ones position.
Multiply 102 by 5. Write the product (510) to the left of the 0.
Add the two products (816 + 5100) to determine the answer.
The correct answer is 102 X 58 = 5,196.

Partial Products Algorithm

75 x 5 = ?
Write the problem vertically.
Multiply (5 x 5). The product is 25. Write 25 as the first partial product.
Multiply (70 x 5). The product is 350. On a new line, write 350 as the second partial product.
Add the two partial products.
The answer is 375.

Lattice Multiplication Algorithm

94 X 7 ?
Write 94 across the top of the lattice. Write the 7 on the right of the lattice.
Follow the 4 down and the 7 to the left. Multiply (4 x 7). The product is 28. Write 28 in the box where 4 and 7 meet. Write the tens digit to the left and above the diagonal, and the ones digit to the right and below the diagonal.
Multiply (9 x 7). The product is 63. In the box where 9 and 7 meet, write 63.
Read the product from left to right around the lattice.
If total of a column is equal to or greater than ten, write the ones digit under that column and write the tens digit at the top of the next diagonal to the left. Add that number to the numbers in that diagonal. The answer is 658.

View the Multiplication of Whole Numbers

Practice

Algorithms

With Base-Ten Blocks

Division by a Two-Digit Divisor

Multiplication and Division in Different Bases

Subtopic