Pre Algebra Period 2

REVIEW

ADDING OR SUBTRACTING FRACTIONS 5-3
NEGATIVE FRACTIONS
1) Double check any subtractions just as you would for integer problems
2) Place the bigger fraction on the top (no matter the sign)
3) Restate to common denominators if needed
4) Borrow if the fraction below is smaller than the fraction above
5) Make sure your answers have consistent signs - In other words, if you have a negative fraction, make sure your whole number part is also negative
OR
1) You can simply make all mixed numbers into improper fractions first
2) Find a common denominator
3) Use integer rules with the numerators
4) Restate back into mixed numbers if required

EXAMPLE using both methods:
5 2/3 - 10 1/4

KEEP THEM AS MIXED NUMBERS:
First of all, you know the final answer will be NEGATIVE so create an answer box right now—and put the negative sign in it!!
Put bigger absolute value on top and take their difference
10 1/4
5 2/3
Find a common denominator:
10 3/12
5 8/12
Borrow because the bottom number is smaller than the top number
9 15/12
5 8/12
Use integer rules to add or subtract:
4 7/12
Put this in your answer box—that you already created with the negative sign and you have
-4 7/12

RESTATE THEM INTO IMPROPER FRACTIONS:
5 2/3 - 10 1/4
17/3 - 41/4

The common denominator is 12
(4)17/(4)(3) - (3)41/(3)(4)

68/12 - 123/12

Subtract using integer rules
-55/12

Restate into a mixed number if required
-4 7/12


EQUATIONS USING ADDING AND SUBTRACTING FRACTIONS 5-7
Same as using adding and subtracting with integers
Use the OPPOSITE (inverse) OPERATION (sign)
If there are fractions on both sides, remember to find a COMMON DENOMINATOR.

EXAMPLE - with a common denominator:
y - 1/8 = 5/8
ADD 1/8 to both sides and you get
y = 5/8 + 1/8 = 6/8
SIMPLIFY to get y = 3/4

EXAMPLE - with different denominators:
y + 4 5/12 = 5 3/8
SUBTRACT 4 5/12 from both sides and get
y = 5 3/8 - 4 5/12
Draw a vertical line separating the whole numbers from the fractions
FIND A COMMON DENOMINATOR which is 24
5 3/8 9/24
-4 5/12 10/24

NOW YOU'LL NEED TO BORROW
4 33/24
-4 10/24
23/24
RESTATE WITH THE VARIABLE FOR YOUR ANSWER y = 23/24

EXAMPLE: When you'll have to double check and put the larger ( absolute value) number on top
y + 2 1/6 = 1 3/8
SUBTRACT 2 1/6 FROM EACH SIDE
y = 1 3/8 - 2 1/6
DOUBLE CHECK , LOOK AND SEE THE SIGNS ARE DIFFERENT—so you will need a SIDE BAR to do your work. PUT THE WINNER ON TOP In this case, PUT 2 1/6 ON TOP (larger absolute value)… Which also means you need to create an answer box with the variable, an equal sign, and the sign of the winner. so on your page you would have in a box y = - just waiting for your results…
- 2 1/6
+1 3/8
Draw a VERTICAL line separating the whole numbers from the fractions
Now you need a COMMON DENOMINATOR:
- 2 1/6 4/24
+1 3/8 9/24

YOU WILL NEED TO BORROW SINCE 9 IS BIGGER THAN 4
At this point I never worry about the signs, I just take their difference—knowing that I have created that answer box with the sign of the answer. ( see above)
2 1/6 4/24
-1 3/8 9/24

1 28/23
1 9/24
19/24
but you put this back in the answer box which is just waiting for your answer and you have y = -19/24
YOU CAN ALSO CHANGE THEM BOTH INTO IMPROPER FRACTIONS FIRST!
y + 2 1/6 = 1 3/8
y + 13/6 = 11/8
-13/6 -13/6
y = 33/24 - 52/24

y = -19/24
ONE OTHER METHOD (that they use in Algebra next year):
GET RID OF ALL DENOMINATORS BY MULTIPLYING BY THE LCD!!!
y + 2 1/6 = 1 3/8
y + 13/6 = 11/8
24(y + 13/6) = 24(11/8)
24y + 52 = 33
-52 -52
24y = -19

y = -19/24




MULTIPLYING AND DIVIDING FRACTIONS 5-4
YOU DO NOT NEED A COMMON DENOMINATOR!!!!

MULTIPLICATION
1. Turn any mixed number into an IMPROPER FRACTION
2. Simplify (Some teachers call this : Cross Cancel) if possible (it makes the math easier!)
3. Multiply numerator x numerator and denominator x denominator
4. Simplify if necessary

DIVISION:
WE NEVER DIVIDE, WE FLIP THE SECOND FRACTION AND MULTIPLY!
(never, ever touch the first fraction!)
1. Turn any mixed number into an IMPROPER FRACTION
2. FLIP THE SECOND FRACTION AND CHANGE TO MULTIPLICATION
3. Cross cancel if possible (it makes the math easier!)
4. Multiply numerator x numerator and denominator x denominator
5. Simplify if necessary

NEGATIVES:
Follow your integer rules to determine the sign

VARIABLES:
You can cross cancel them as well!


EQUATIONS USING MULTIPLYING AND DIVIDING FRACTIONS 5-8
SOLVING ONE STEPS WITH FRACTIONS THAT ARE MULTIPLIED
SIMPLY MULTIPLY BY THEIR RECIPROCAL
3/5 y = 20
(5/3)(3/5)y = 20(5/3)
y = 100/3
Make mixed if required: 33 1/3

MIXED NUMBERS?
TURN THEM INTO IMPROPER, THEN MULTIPLY BY RECIPROCAL
4 2/3 y = 2 1/6
14/3 y = 13/6
(3/14)(14/3) y = (13/6)(3/14)
y = 13/28