Transcript Combining Signed Numbers

Equations with
Fractions
YUCK!
x x2

7
2
6
What to do? What to do?
Let’s get rid of the dang fractions!
Remember the miracle of multiplying fractions:
CANCELLATION!
Cancellation
1
If you multiply by 2, you get
2
1
1 2 1 2
2     1
2
2 1 2 1
Cancellation
If you multiply
5
6
by 6, you get
5
5 6 5 6
6      5
6
6 1 6 1
Getting rid of 2 denominators
We have to get rid of both a 2 and a 6.
What number can we multiply by that
will cancel both of them?
The Least Common Denominator!
LCD
Unless someone flat out asks you what
the least common denominator is, you
can really use any common
denominator in most fraction
problems. They just like to use the
smallest one to keep the numbers in
the problem small.
LCD and Least Common Multiple
If thinking of the LCD makes your eyes
cross, go for the least common multiple
instead!
Multiples of 2: 2, 4, 6, 8, 10, 12
Multiples of 6: 6, 12, 18, 24, 30
Least Common Multiple
Smallest number on both lists:
Multiples of 2: 2, 4, 6, 8, 10, 12
Multiples of 6: 6, 12, 18, 24, 30
Common Multiples
Notice that there are other numbers on
both lists:
Multiples of 2: 2, 4, 6, 8, 10, 12,…,18
Multiples of 6: 6, 12, 18, 24, 30
You could use any of these to get rid of
the fractions in your equation.
Let’s Multiply by 6!
x x2

7
2
6
You have 2 terms on the left
and 1 term on the right.
 x  x2
 
7
2  6 
So you'll need three 6's.
Let’s Multiply by 6!
x x2

7
2
6
6 x 6 x2
  
 6  7 Don't forget the 7!
1 2 1 6
36 x 6 x  2
  
 67
1 2 1 6
3x  x  2  42 Now, isn't that easier?
Wrap-up
3x + x + 2 = 42
4x + 2 = 42
4x = 42 – 2
4x = 40
X = 10
Check
10 10  2

7
2
6
12
5  7
6
5 2  7
77
check!
Minus Signs Between Fractions
4( x  3) x  2 1


5
15
3
15 4( x  3) 15 x  2 15 1 Cancel the fractions!
(
) (
) ( )
1
5
1 15
1 3
(3)(4)( x  3)  ( x  2)  5
12( x  3)  ( x  2)  5
12 x  36  x  2  5
13 x  34  5
13 x  39
x  3
Distribute the -1
Dreaded Fractions
Any time you have an equal sign and
fractions:
Determine a common denominator
Multiply each term by it.
If all your fractions don’t cancel, you
picked the wrong number!.