1. Equivalent Fractions A fraction shows:#1
A fraction shows:
Numerator
Parts Shaded
Denominator
Total Parts
Equivalent fractions name the same amount or the same part of a whole. You use the giant one to show equivalent fractions.
Ex:

2. Giant One/ Simplest Form#2
Giant One/ Simplest Form
The Giant One is used to reduce or simplify fractions.
To find the simplest form divide the numerator and denominator by the greatest common factor.

3. Mixed Number 1 = = Improper Fraction #3 3 4 8 4
A mixed number has a part that is a whole number and a part that is a fraction. 1 3 = 4
Improper Fraction
An improper fraction is when the numerator is greater than the denominator.
1/4
1/4
numerator
1/4
1/4 8 = 4
denominator
1/4
1/4
1/4
1/4

4. = 2 ) 2 5 5 2 1 2 #4 How To Change An Improper
Fraction To a Mixed Number 5 = 2
Divide the numerator by the denominator.
Put your remainder over the denominator. 1 2 2
denominator ) 2 5
numerator

5. Number To An Improper Fraction#5
How To Change A Mixed
Number To An Improper Fraction 1 9 +
1) Multiply the whole number times the denominator.
2) Add your answer to the numerator.
3) Put your new number
over the denominator. 4 = x 2 2

6. Least Common Denominator#6
Least Common Denominator
TO FIND THE LCM OF 4 and 12:
1) List the multiples of both numbers
4 = 4, 8, 12, 16, 20…
12 = 12, 24, 36…
2) Find the least multiple that both numbers have in common.
LCM is 12
Least Common Multiple is also known as LCD.

7. Comparing Fractions > #7 < >
Read these symbols from left to right.
<
Less than
>
Greater than
Less than or equal to
Greater than or equal to
****************************************************************
To compare fractions you must show your work!
>

8. Add Fractions With The Same Denominator#8
Add Fractions With The Same Denominator -2 6 3 6
You ADD numerators + 6 1
The denominator STAYS THE SAME!

9. EQUIVALENT FRACTIONS OF#9

10. One-Third Plus Two-Fourths
#10
One-Third Plus Two-Fourths
Giant One
horizontal 1 3 4 12
• 4 =
vertical 6 12 2 4
• 3 = + 10 12 5 6

11. 1 Add Fractions 12 4 15 5 10 2 + 3 15 22 15 #11 x 3 = x 3 = x 5 =
Find a common denominator. 15 5
x 3 = 10 2
2) Add the numerators.
x 5 = + 3
x 5 = 15
3) Keep the common denominator the same. 22 7 1 15 15
4) Simplify or reduce. Change improper fractions to mixed #s.
15) 22 15 7

12. - Subtract Fractions 5 x 4 = 20 6 x 4 = 24 1 x 3 = 3 x 3 = 8 24 17 24
#12 5
x 4 = 20 6
x 4 = 24
Always SHOW
YOUR WORK!
This includes the
Giant One. 1
x 3 = 3 -
x 3 = 8 24 17
Giant One 24

13. Add Mixed Numbers
#13 1 5 20 11
x 4 = 24 1 6 24
x 4 = 24 5 15
x 3 =
24) 35 3 + 8
x 3 = 24 24 28 11 35 11 24 24
IMPROPER

14. One-Third of a Negative One-Half Piece
#14
Draw one-third (horizontal)
Draw negative one-half (vertical) 1 3 -1 2
What is of ? Draw a picture (overlay them).
+ • – = –

15. Multiply
#15
You do NOT need common denominators 
Multiply the numerators and denominators straight across. 7 4 28
Change the improper fraction to a mixed number = 2 3 6 4 4
Reduce! 6 6) 2 28 4 2 = 4 4 ÷ 24 3 6 2 ÷ 4

16. Multiply Mixed Number Directions
#16
Multiply Mixed Number Directions
You DO NOT need common denominators 
1. Change the mixed numbers to improper fractions.
2. Multiply the numerators straight across.
3. Multiply the denominators straight across.
4. Simplify or reduce if possible.

17. Multiply Mixed Numbers
#17
Multiply Mixed Numbers
35+4 4 39 39 1 + 5 = 4 7 7 28 x 35 11
IMPROPER 1 28
28) 39

18. 5 2 17 3 3 17 3 = #18 Reciprocals 2 5 1 10 Example: X = = - - - 5 2 10
Two numbers are reciprocals if their product is one. 2 5 1 10
Example: X = = - - - 5 2 10
To find the reciprocal just flip the fraction over.
Change your mixed number to an improper fraction to find the reciprocal. + 2 17 3 5 = 3 17 x 3

19. Divide 3  There are 12 one-fourths that fit into 3.
#19
1) Draw a picture to show 3 wholes.
2) How many ’s fit into 3 wholes?
There are 12 one-fourths that fit into 3.

20. Dividing Fractions
#20
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
Example: 1 5 5 2 5 3 1 1 . X = = = - - - - - - - 6 3 6 2 4 4 . 2 .

21. Subtract Mixed Numbers
#21
Subtract Mixed Numbers 4 2 30 =
1st: Change your mixed numbers to improper fractions. 7 7 - 1 6 13 = 7 7
2nd: Subtract numerators. 17
3rd : The denominator
stays the same. 2 3 7 7
4th : Change your
answer to a mixed
number. 7) 17 14 3

22. #22
FRACTION REVIEW
Add Fractions: Find a common denominator. Add the numerators, and keep the denominator the same.
Subtract Fractions: Find a common denominator. Subtract the numerators, and keep the denominator the same.
Multiply Fractions: Multiply the numerators and denominators straight across.
Divide Fractions: Multiply the first fraction by the reciprocal of the second fraction.
Mixed Numbers: Change it to an improper fractions first.

23. Add Fractions 12 4 15 5 -10 -2 + 3 15 2 15 #23 x 3 = x 3 = x 5 = x 5 =
Find a common denominator. 4
x 3 = 15 5
x 3 =
2) Add the numerators.
-10 -2
x 5 = +
3) Keep the common denominator the same. 3
x 5 = 15 2
4) Simplify or reduce. Change improper fractions to mixed #s. 15

24. Add & Subtract Negative Fractions
#24 -2 -4 -4 -8
x 2 =
x 2 = 6 12 5 10
x 2 =
x 2 = 3 9 1 1
x 3 =
x 1 = - + 4
x 3 = 12 10
x 1 = 10 5 -9
-8 – 1 = = 12 10 -9

25. Multiply Negative Fractions
#25
You do NOT need common denominators 
Multiply the numerators and denominators straight across.
-20 -5 4
Change the improper fraction to a mixed number! = 2 3 6 2 -3
Reduce! 6 6) 1
-20 -3 2 = 2 -3 ÷ 18 3 6 2 ÷ 2

26. Divide Negative Fractions
#26
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
Example: 1 -5 -5 -5 3 1 -2 1 . X = = = - - - - - - - 6 3 6 1 2 2 . 2 .

27. Reciprocals
#27
To write a reciprocal of a mixed number, you must change your mixed number to an improper fraction first.
-42 -5 + 2 = 8 x 8
FLIP IT OVER!
Then write the reciprocal of your improper fraction. -8
-42 8 42

28. Extras

29. One-Third of a One-Half Piece
#Extra
One-Third of a One-Half Piece
Draw one-third (horizontal)
Draw one-half
(vertical) 1 3 1 2
What is of ? Draw a picture (overlay them).

30. Two numbers are reciprocals if their product is one.#
Two numbers are reciprocals if their product is one. 1 2 5 10 X
Example: = = - - - 5 2 10
To find the reciprocal just flip the fraction over.

31. Write the Reciprocal of a Mixed Number#
To write a reciprocal of a mixed number, you must change your mixed number to an improper fraction first. 17 + 2 5 = 3 x 3
Then write the reciprocal of your improper fraction. 3 17 17 3