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FRACTIONSDefinition:
A fraction is a part of a whole.
TABLE OF CONTENTS
REDUCING 16
MIXED NUMBERS/IMRPOPER FRACTION 12
RECIPROCALS 15
COMMON DENOMINATOR 14
SUBTRACTING AND ADDING 3 AND 4
MULTIPLYING AND DIVIDING 7 AND 9
WORD PROBLEMS 13
S E C T I O N 1 . A D D I N G , S U B T R A C T I N G , M U LT I P LY I N G A N D D I V I D I N G F O R
F R A C T I O N S
Adding: For adding fractions together you have to have common denominators
so that all you have to do is add the numerators.
Problems
1. 1/5+3/5=4/5 8. 3/4+1/4=1 or 4/4
2. 2/6+3/6=5/6 9. 9/12+ 2/12=11/12
3. 1/4+1/4=1/2 10.1/4+2/4=3/4
4. 1/2+1/3=5/6
5. 5/6+1/6=1 or 6/6
6. 1/4+ 1/12=1/3
7. 6/10+3/10=9/10
SUBTRACTION…?
Subtracting: For subtracting fractions you
have to first find the lowest common
denominator, then you multiply the
numerators first and then subtract them
when both denominators are the same.
SUBTRACTION.....?
Subtracting: For subtracting fractions you have to first find the lowest common
denominator, then you multiply the numerators first and then subtract them when both
denominators are the same.
10/12-4/12= 10-4=6/12 reduced=1/2
Step 1:For subtracting fractions you first have to find the lowest common denominator.
Step 2: Second you would have to multiply the numerators.
Step 3: the subtract them when both denominators are the same.
SUBTRACTION….?
Problems:
1. 5/9-1/6 6. 10/11-5/11
2. 3/4-1/4 7. 7/12-5/12
3. 1/2-1/6 8. 8/10-5/10
4. 2/4-1/49. 11/12-3/12
5. 6/11-5/11 10. 10/20-5/20
MULTIPLICATION….?
Multiply: For multiplying fractions together you have to first multiply the numerators of
each fraction then multiply the denominators for the answer.
8/10*4/6= 8*4=32 10*=60 32/60=8/15
Step1. First you multiply the numerators together.
Step2. second you would multiply the denominators to get the answer.
MULTIPLICATION
Multiply: For multiplying fractions together you have to first multiply the numerators of each
fraction then multiply the denominators for the answer.
Problems:
1.3/4*2/3= 7.1/2*3/6=
2.1/9*6/7= 8.1/4*9/10=
3.1/2*3/7= 9.4/10*1/6=
4.3/6*2/4=
5.7/10*3/6=
6.3/4*5/6=
DIVISION….?
Division: To divide fractions you first reciprocate the second fractions and then multiply the numerators together and the denominators and get the answer .
1/108/6= 1/10*6/8=6/80 Reduced = 3/40
Step 1: First you need to change the division sign to a multiplication sign .
Step 2: Second you have to reciprocate the second fraction for example
8/6 changes to 6/8.
Step 3: Third you have to multiply the numerators and denominators
together to the answer.
DIVISION…?
Problems:
1. 1/21/6= 6. 3/46/10=
2. 1/8= 7. 1/41/5=
3. 5/61/3= 8. 1/41/10=
4. 10/121/6= 9. 1/101/12=
5. 2/31/4= 10. 7/81/5=
M I X E D N U M B E R S / I M P R O P E R F R A C T I O N S
To change mixed numbers into improper fractions
you have to first multiply the denominator by the
whole number. The next thing you have to do is take
the answer of the denominator multiplied by the
whole number and add the numerator by it. And you
get the improper fraction.
M I X E D N U M B E R / I M P R O P E R F R A C T I O N
Example: Find the improper fraction.
1. 3 6. 2
2. 6 7. 5
3. 8 8. 8
4. 6 9. 9
5. 7 10. 9
WORD PROBLEMS
To do word problems you have to put the numbers in
the problem into the word problem.
Examples:
Two friends both have cookies and the want to see
how many they have. So Madison had 12 cookies and
Shelby had 20 cookies. They added them together
and got 32 cookies altogether.
COMMON DENOMINATORTS…..?
For common denominators you have to first find the
denominators by multiplying both of the
denominators by the same number that makes them
the same. Then you get the common denominators of
both fractions.
RECIPROCALS…?
To reciprocate you have to flip the fraction the other
way,
1/5…………… 7\12……………..
2/6…………… 9\24……………...
5/9......................... 3\6………………
9\18……………… 9\15…………….....
6\12……………….. 8\14……………........
REDUCING
TO REDUCE FRACTIONS YOU HAVE TO FIRST
FIND A NUMBER THAT IS DIVISIBLE BY THE
NUMERATOR AND DENOMINATOR. THEN DIVIDE
THE NUMEATOR AND DENOMINATOR BY THE
NUMBER.
ANSWER KEY
PAGE 3 PAGE 6
1. 4/5 1. 7/18
3. ½ 3. 2/6
5. 1 OR 6/6 5. 1/11
7. 9/10 7. 5/12
9. 11/12 9. 8/12
ANSWER KEY
PAGE 8 PAGE 10
1. ½ 1. 3
3. ¼ 3. 8/3
5. 7/20 5. 5/2
7. ¼ 7. 35/8
9. 1/15 9. 6/5
ANSWER KEY
PAGE 12 PAGE 15
1. 13/4 1. 5/1
3. 68/8 3. 9/5
5. 47/6 5. 12/9
7. 112/20 7. 24/9
9. 87/9 9. 15/9