1. Unit 2 Common Fractions

2. 2 FRACTION A fraction is a value that shows the number of equal parts taken of a whole quantity or unit  Fractions can be expressed in lowest terms by dividing both the numerator and denominator by their greatest common factor  To reduce to lowest terms, divide both the numerator and denominator by 5

3. 3 MIXED NUMBERS AS FRACTIONS A mixed number is a whole number plus a fraction To express a mixed number as an improper fraction:  Find number of fractional parts contained in the whole number  Add the fractional part to the whole number equivalent

4. 4 MIXED NUMBERS AS FRACTIONS Find the number of fractional parts contained in the whole number  Add the fractional part

5. 5 FRACTIONS AS MIXED NUMBERS To convert fractions into mixed numbers, divide and place the remainder over the denominator 64 11

6. 6 ADDITION OF FRACTIONS Requires a common denominator Least common denominator is smallest number that all denominators divide into evenly First, determine the LCD: 6 = 2 × 3; 3 = 1 × 3; 15 = 3 × 5 LCD = 2 × 3 × 5 = 30

7. 7 ADDITION OF FRACTIONS Next, convert every fraction to 30ths:

8. 8 ADDITION OF FRACTIONS Finally, add the numerators of the fractions and convert to a mixed number:

9. 9 SUBTRACTION OF FRACTIONS Subtraction of fractions requires a common denominator. First, determine the prime factors of each denominator: 16 = 2 × 2 × 2 × 2 8 = 2 × 2 × 2

10. 10 SUBTRACTION OF FRACTIONS Then determine the LCD: 2 × 2 × 2 × 2 = 16 Next, convert 3/8 to 16ths:

11. 11 SUBTRACTION OF FRACTIONS Finally, subtract the numerators of the fractions:

12. 12 LOWEST COMMON DENOMINATORS  Use prime factoring when LCD is difficult  Factor each denominator into prime factors  List each prime factor the most times it appears in any one denominator  Multiply all the prime factors listed

13. 13 LOWEST COMMON DENOMINATORS (Cont)  Find the lowest common denominator:  Prime factor each denominator

14. 14 LOWEST COMMON DENOMINATORS (Cont) List each prime factor the most times it appears in any one denominator 3 × 3 × 2 × 5 × 5 Multiply the factors 180 Ans

15. 15 MULTIPLICATION OF FRACTIONS Multiplication and division of fractions do not require a common denominator To multiply simple fractions, multiply the numerators and multiply the denominators Mixed numbers must be changed to improper fractions before multiplying

16. 16 MULTIPLICATION OF FRACTIONS

17. 17 MULTIPLICATION OF FRACTIONS

18. 18 DIVISION OF FRACTIONS To divide fractions, invert the divisor, change to the inverse operation, and multiply.

19. 19 DIVISION OF FRACTIONS First, change Next, divide

20. 20 ORDER OF OPERATIONS As with any arithmetic expression, the order of operations must be followed. The operations are:  Parentheses  Exponents  Multiplication and division from left to right  Addition and subtraction from left to right

21. 21 ORDER OF OPERATIONS First, addition in ( ) Next, division

22. 22 PRACTICE PROBLEMS 1. Reduce each of the following: a.b.c. 2. Express these mixed numbers as improper fractions: a.b.c. 3. Express these improper fractions as mixed numbers: a.b.c.

23. 23 PRACTICE PROBLEMS (cont.) 4. Perform the indicated operations:

24. 24 PRACTICE PROBLEMS (cont) 4. Perform the indicated operations:

25. 25 Practice Problems 5. Calculate dimensions A-E using the template

26. 26 Solutions 1. Reduce a. A b. B c. C 2. Mixed to improper a. A b. B c. C 3.Improper to mixed a.A b.B c.4

27. 27 Solutions 4.operations a.A b.B c.C d. A e. B f. C g. A h. B i. C j. D

28. 28 Solutions 5.template A.A B.B C.C D.A E.B