Lesson 5: Fractions Per 3, 5: 10/5/15 Per 2, 4, 6: 10/6/15

Lesson Objectives: SWBAT… add, subtract, multiply, and divide fractions with like and unlike denominators. SWBAT…convert an improper fraction to a mixed number. And convert mixed numbers to improper fractions and simplify when necessary. SWBAT…write the prime factorization form of fractions and provide the lowest common denominator.

Adding/ Subtracting Fractions w/ like denominators: Keep the denominators the same and add or subtract the numerators. Examples: 2 + 1= = 4 =

Whiteboard CFU You need a nail that goes through a 5/8- inch door and will stick out 1/8 inch on the other side. How long does the nail have to be?

Answer: 5/8 + 1/8= 6/8= 3/4

Add/Subtract Fractions w/ unlike denominators: You must find a common denominator: Examples: = = = =

Mixed Numbers/Improper Fraction: We first add the whole numbers together, and then the fractions.

Whiteboard CFU Add

Answer: 1/2 + 2/3 =3/6 + 4/6 =7/6 = 1 1/6

Whiteboard CFU Subtract. 3 – 1 4 6

Answer: 3/4 – 1/6 =18/24- 4/24 = 14/24 = 7/12

Multiply Fractions: Multiply straight across. Reduce when necessary. Example: 4 X 2 =

Multiply Fraction X Whole Number: Example: 4 X 8 = 4 X 8 = Helpful Hint: Must convert all improper fractions into mixed numbers!

Multiply Mixed Numbers: Multiply. 1 ¾ X 2 ¼ Step 1: Rewrite the mixed numbers as fractions 7 X 9 4 Step 2: Multiply straight across =63 16 Step 3: Turn improper fraction to mixed number =3 15/16

Whiteboard CFU Multiply. 1 X 3 2 4

Answer: 1/2 X 3/4 = 3/8

Whiteboard CFU Multiply. 1 ¾ X 2 2/3

Answer: 1 ¾ X 2 2/3 = 7 X = = 4 2/3

Dividing Fractions: Multiply the first fraction with the reciprocal of the second fraction. Example: 2/5 ÷ 1/4= 2 X 4 =

Example: 2/3 ÷ 1/5 = 2/3 X 5/1 =10/3 =3 1/3

Whiteboard CFU 3 1/3 ÷ 1 1/2

Answer: 3 1/3 ÷ 1 1/2 = 10/3 ÷ 3/2 = 10 X = 20 9 = 2 2/9

Prime Factorization to find lowest common denominator: Prime Number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, , etc

Prime Factorization to find lowest common denominator: Step 1: Find the factors of each denominator. 10= 2  5 15= 3  5 Steps 2: Since the common prime factor is 5 and the additional factors are 2 and 3, the prime factors of the lowest common denominator is 2  3  5

The prime factored form of the LCD of is 2  3  5 so the LCD is

Whiteboard CFU: Find the prime factored form of the lowest common denominator of

12= 2  2  3 6= 2  3 Prime Factored Form=2  2  3 LCD=12