1. Chapter 4 - Fractions
FRACTIONS
A proper fraction is a fraction whose numerator is less than its denominator.
Proper fractions have values that are less than 1.
An improper fraction is a fraction whose numerator is greater than or equal to its denominator.
Improper fractions have values that are greater than or equal to 1.

2. Improper fractions can be converted to a mixed number.3 4
= 5
Same denominator.
-20
3(R)
Mixed numbers

3. TRY THIS!

4. Solutions

5. Simplifying (Reducing) Fractions
Determine if BOTH the numerator and the denominator share any common factors
Divide the numerator and the denominator by the same number
Check if you can reduce further. Your answer should be in the lowest terms.

6. Which fraction can be reduced?

7. Which fraction can be reduced?
No!
No!
Common factor: 5
Common factor: 3
Yes!
Yes!

8. Chapter 4 - Fractions
Equivalent Fractions

9. Multiplying Fractions
TOP x TOP 1 2
Bottom x Bottom
Always Reduce 1st!!!!

10. Multiplying Fractions
Reduce before multiplying (if possible)
Multiply straight across the numerator and denominator
Don’t forget about the sign, if any.
Check if you can simplify your answer

11. TRY THIS! STEPS 1. Reduce Multiply Across Check if the answer
is in the lowest terms

12. SOLUTIONS 1 STEPS 1. Reduce Multiply Across Check if the answer
TOP x TOP 1
STEPS
1. Reduce
Multiply Across
Check if the answer
is in the lowest terms 1 2 1
Bottom x Bottom 1 1 3 6

13. FLIP = INVERT = RECIPROCATE the fraction
DIVIDING FRACTIONS
DIVIDING BY A FRACTION IS AS SIMPLE AS , YOU FLIP AND MULTIPLY!!!!!!!!
PIE
(1. Keep the first fraction), (2. Change division to multiplication), (3. Flip the second fraction) 1 4
FLIP = INVERT = RECIPROCATE the fraction

14. Dividing Fractions Keep the first fraction
Change the division sign to multiplication
Flip the second fraction
Multiply fractions across the numerator & denominator
Follow integer rules for multiplication
Check if you can simplify your answer

15. Adding and Subtracting Fractions
You must have a COMMON DENOMINATOR in order to add and subtract fractions
Add/Subtract the numerators
Keep the same denominator
Follow integer rules for addition and subtraction
Check if you can reduce your answer
To find the LEAST COMMON DENOMINATOR (LCD), use:
Guessing,
or Listing Multiples,
or Prime factorization of denominators

16. SUBTRACTING FRACTIONS W/UNLIKE DENOMINATORS
MULTIPLY BY
RATIO OF ONE 3
1. LCD =?
3. SUBTRACT ACROSS KEEP BOTTOM 1 9

17. TRY THIS!

18. SOLUTION. 5 21

19. MULTIPLY MIXED NUMBERS3 3 1 1
1. IMPROPER
1. IMPROPER
2. REDUCE BEFORE MULTIPLYING

20. DIVIDING MIXED NUMBERS7
1. IMPROPER
1. IMPROPER
2. FLIP & MULTIPLY
3. REDUCE 5

21. ADDING MIXED FRACTIONS

22. ADDING MIXED NUMBERS (Alternative Method)
∙ 2
∙ 2
1. LCD
∙ 3
1. LCD
∙ 3
MIXED

23. SUBTRACTING MIXED NUMBERS

24. SUBTRACTING MIXED NUMBERS (Alternative Method)
1. LCD BORROWING
∙ 2
∙ 2
∙ 3
∙ 3

25. COMPLEX FRACTIONS
A FRACTION IN THE NUMERATOR OR DENOMINATOR

26. COMPLEX FRACTIONS (ALTERNATIVE WAY)
A FRACTION IN THE NUMERATOR OR DENOMINATOR
LCD = 15
2. MULTIPLY BY LCD EACH TERM 5 3
 15 1
15  1 5 1
15  1
 15 1
3 STEPS
LCM/LCD
MULTIPLY EACH TERM IN TOP & BOTTOM BY LCD
(DISTRIBUTIVE PROPERTY)
3. SIMPLIFY