Download Improving on your textbook24: Creating the Lacking Factors (Lacks

Improving on your textbook24:
MrV sometimes requires notations and techniques that are not covered completely in the text.
These should always be used in your homework, tests and quizzes.
Chapter 2.4 – An Extended LCM Primes Table makes adding fractions easier.
The textbook does a good job showing you how to build LCM Primes Tables. Section 2.4 shows you how to
add fractions with different denominators by finding the Least Common Denominator. By adding a Lacking
Factors column to the right, we can quickly find the multipliers needed.
Creating the Lacking Factors (Lacks↓) column:
1. Create the LCM primes table for the fraction denominators, and determine the LCD (LCM).
2. Add a column to the right and give it the heading Lacks↓
3. For each denominator row:
a. List all additional factors needed to match the LCD.
b. Multiply them together (if necessary) to get a single number.
4. Use the Lacks column numbers to multiply the corresponding fractions, top and bottom.
Example:
Original Problem:
Another Example:
3
7

20 30
Use Primes Table to find LCD,
then find the Lacks for 20 and 30
Multiply each fraction
top/bottom by its Lack
3
33

20
20  3
7
72


30
30  2
3
33
9


20
20  3 60
7
7  2 14



30
30  2 60
Add the multiplied tops,
23
and put the sum over the LCD
60
Change to a mixed number (if needed),
Simplify the fraction part (if needed)
Multiply each top
and put it over the LCD
Original Problem:
1 2 7
 
3 9 8
Use Primes Table to find LCD,
then find the Lacks for 20 and 30
Multiply each fraction
top/bottom by its Lack
Multiply each top
and put it over the LCD
1 1  24

3 3  24
2 28

9 98
7 79
 
8 89
1 1  24 24


3 3  24 72
Add the multiplied tops,
2 28
16


and put the sum over the LCD
9 98
72
Change to mixed number,  7  7  9  63
8 8  9 72
Can’t be reduced
103
31

1
72
72