Lining Up by Place Value

Lining up by place value is a method used to compare and perform arithmetic operations on whole numbers. This method involves aligning the digits of two or more numbers according to their place value, with the digits in each column representing the same place value. For example, when adding the numbers 123 and 456, we would align the digits as follows:

123
+ 456
-----

We would then add the digits in the rightmost column (3 and 6), which gives us 9. We would then move to the next column to the left and add the digits in that column (2 and 5), which gives us 7. Finally, we would add the digits in the leftmost column (1 and 4), which gives us 5. Therefore, the sum of 123 and 456 is 579.

Lining up by place value is also used when comparing numbers. For example, when comparing the numbers 123 and 456, we would align the digits as follows:

123
  456

We would then compare the digits in the leftmost column (1 and 4), and determine that 4 is greater than 1. Therefore, 456 is greater than 123. Lining up by place value is an important concept in mathematics and is used in various operations, including addition, subtraction, multiplication, and division.