The document discusses various operations involving fractions, including simplifying, converting between mixed and improper fractions, multiplying, dividing, adding, and subtracting fractions. It provides examples of performing each operation step-by-step and simplifying the resulting fraction. Rules for working with fractions are reviewed and examples of applying the rules are shown.

1. Review on
FRactions
Simplification of Fractions/
Operations on Fractions

2. 40
Simplifying
10 Reduce
4 ⋅ 10 4
= = = 4
1 ⋅ 10 1
10 = Greatest Common Factor
Write the numerator and denominator as a product of factors,
then cancel common factors and obtain the result.

3. 16
Simplifying
72
4⋅4 4 2⋅2 2
= = = =
4 ⋅ 18 18 2⋅9 9
Write the numerator and denominator as a product of common
factors then cancel the common factors and obtain the result.
Repeat the simplification process until all common factors are removed.

4. Converting Mixed Numbers
1
5
3
• + 16
=
3
Multiply the whole number by the denominator
Add the numerator to the result
Place over the initial denominator
Compute the final result

5. Converting Mixed Numbers
2
6
9
• + 56
=
9
Multiply the whole number by the denominator
Add the numerator to the result
Place over the initial denominator
Compute the final result

6. Multiplying
3 10
⋅
3 10⋅ 3 2 5 15 ⋅ ⋅
8 11
=
8 11⋅= =
4 2 11 44 ⋅⋅
a c ac
⋅ = Fraction Multiplication
b d bd
Fraction Simplification

7. Multiplying
2 15
⋅
2 15⋅ 2 3 5 5 ⋅ ⋅
3 4
=
3 4 ⋅=
3 2 2
=
2 ⋅⋅
a c ac
⋅ = Fraction Multiplication
b d bd
Fraction Simplification

8. Dividing
12 3 12 3•4 7 28
÷ = • = •
3
=
5 7 5 5 5
a c a d
÷ = ⋅ Fraction Division
b d b c
Fraction Simplification and Multiplication

9. 4 8
Dividing 4
5
÷ 15
=
24 8 24 3•8 3•5
÷ = • = •
8
5 15 5 5
9
= = 9
1
a c a d
÷ = ⋅ Fraction Division
b d b c
Fraction Simplification
Fraction Multiplication
Mixed Number Conversion

10. Adding/Subtracting
Fraction Simplification
3 - 1 2 = 1
= = 8
8 8 4
8
a b a±b
± = Fraction Addition/Subtraction
c c c

11. Adding/Subtracting
11 2 = 11 + 2 •??? 11 + 8
11 2 4
+ 7 28 + 7 • 4 = 28 28
28 28 + 7
= 11 + 8 = 19
28 28 28
a b a±b
Common =
± Denominator = ??????
Fraction Addition/Subtraction
c c c

12. Rules of Fractions Review
• Fraction Simplification
• Mixed Number Conversion
• Fraction Multiplication
• Fraction Division
• Fraction Addition/Subtraction

13. 21
YOU TRY IT 13
8 45
3 1 5 4
2 + −
8 4 9 15
3 12 5 4
⋅ ÷
2 15 12 3
6 5
5 16

14. Fractions: Steps for Success
1. Know the fraction rules and how to apply
them
2. Show your work and write out each step
3. Check your work for errors or careless
mistakes

15. 3 1 19 + 1
2 + = Mixed Number Conversion
8 4 8 4
19 + 2 Fraction Addition
=
8 8
21
= Fraction Addition
8

16. 5 4 25 - 12
− = Fraction Subtraction
9 15 45 45
13
= Fraction Subtraction
45

17. 3 12 3 3 • 4 Fraction Simplification
⋅ =
2
•
2 15 3•5
3 4
= • Fraction Simplification
2 5
3 2 • 2 Fraction Simplification
= •
2 5
3 2 Fraction Simplification
= 1 •
5
6
= 5 Fraction Multiplication

18. 5 4 5 3
÷ = • Fraction Division
12 3 12 4
5 3
= 3•4 • 4 Fraction Simplification
5 • 1
= Fraction Simplification
4 4
5
= Fraction Multiplication
16