What is an expanded algorithm? Son doesn't know and didn't bring home his textbook, any ideas?
Check these sites.
http://www.atlantatraffic.com/KSUWebsite/?p=825
http://math-ed.com/NO/NO_2_4_reading.htm
Usually used with multiplication, creating an expanded algorithm is taking a formula and "drawing it out," or making it longer (and thus more simplified) by "un-distributing" it. For example:
Expand (a+b)n.
Answer: an + bn
Why: In the problem, n should be distributed to both a and b using the Distributive Property of Multiplication.
Example #2:
Expand (2+4+9)10.
Answer: 20+40+90, or 150
Why: See above.
Hope this helps!
An expanded algorithm is a method used in arithmetic to perform calculations by breaking down numbers into their place values. It is commonly used in multi-digit addition, subtraction, multiplication, and division.
To explain how an expanded algorithm works, let's consider an example of multi-digit addition:
Suppose we want to add two numbers: 345 and 178.
1. We start by writing the numbers vertically, with the digits lined up according to their place value:
345
+ 178
2. We then begin adding the digits from the rightmost place value (ones place) and move leftwards:
345
+ 178
-----
Starting with the ones place, we add 5 + 8, which equals 13. Since 13 is a two-digit number, we write down the ones digit (3) in the ones place and carry over the tens digit (1) to the next column.
3. The next column to add is the tens place:
345
+ 178
-----
3
+ 1
We add the carried-over tens digit (1) to the sum and the digit in the tens place (4). 1 + 4 equals 5. So, we write down 5 in the tens place.
4. Finally, we add the hundreds place:
345
+ 178
-----
53
There are no more place values to add, so we write down the sum, which is 53, below the line.
Therefore, the sum of 345 and 178 is 523.
By breaking down the addition process into smaller steps based on place values, the expanded algorithm helps in understanding each step of the calculation and helps prevent mistakes. The same concept applies to subtraction, multiplication, and division as well, where you break down the calculations based on place values and perform the operation step by step.