Fractions

Definitions Fraction: a quotient of two numbers Numerator: the top number of a fraction Denominator: the bottom number of a fraction Example: ⅝ 5 is the numerator 8 is the denominator

Examples of Prime numbers 2,3,5,7,11,13,17,19,23,29,31…… Prime number: A whole number, other than one, whose factors are one and itself Two numbers multiplied together are factors (5)(3) = 15 5 and 3 are factors Examples of Prime numbers 2,3,5,7,11,13,17,19,23,29,31…… 2 is the only even prime number Why? Every other Even number has a factor(can be divided) by 2!

Other composite numbers: 12, 8, 4, 15, 21, 24, 33, 81…… Composite Numbers: Integers that can be written as a product of 2 prime numbers, other than one and itself Example: 10 = (5)(2) Other composite numbers: 12, 8, 4, 15, 21, 24, 33, 81……

How to write a composite number as a product of primes First write the number as a product. (think of two numbers that multiply to that number) If both numbers are prime then you are done, if not you need to break down each composite number. Factor Tree: 30 ^ 5 ∙ 6 2 ∙ 3 So 30 = 5 ∙ 2 ∙ 3

Write each composite number as a product of primes! 40 63 81 Answers 40 = (2)(2)(2)(5) 63 = (7)(3)(3) 81 = (3)(3)(3)(3)

Writing Fractions in Lowest Terms Using Product of Prime Numbers Write the numerator and the denominator as a product of prime 2. Cancel out any number that is in the numerator and the denominator 24 = (2)(2)(2)(3) 72 (3)(2)(2)(2)(3)

Multiply the remaining numbers in the numerator together Multiply the remaining numbers in the numerator together. If there is no numbers left, then use 1 Multiply the remaining numbers in the denominator together. If there is no numbers left, then use 1 ANSWER 1 3

Examples: 20 35 24 70 20 = (2)(2)(5) (5)(7) 35 (5)(7) 20 = 4 35 7 35 (5)(7) 20 = 4 35 7 24 = (4)(3)(2) 70 (7)(2)(5) (7)(2)(5) 24 = 12 70 35 Examples: 20 35 24 70

Writing Fractions in Lowest Terms by writing it as a Product First, think of a common factor that the numerator and denominator both have. Example: 24 108 Second, write the numerator and the denominator as a product using that common factor. Third, Cancel out the common factor. Check to see if the new numerator and denominator have any common factors. If not, then it is in lowest terms. If not repeat the first and second steps.

Writing Fractions in Lowest Terms as a Product First write you numerator and denominator as a product using a common factor Second cancel out any common factors Repeat for the remaining factors If you cannot repeat then your fraction is in lowest terms Example: 16 18

Operations with Fractions Multiplying Fractions A ∙ C = A∙C B D B∙D B and D cannot equal zero. Multiply the numerators together and the denominators together Then write your answer in lowest terms Example: 2 ∙ 3 = 6 7 10 70

Example: Page 21 # 19-22 19). ½∙¼ 20). 10 · 3 21). 2 · 3 22). 7 ∙ 3 19). ½∙¼ 20). 10 · 3 6 5 21). 2 · 3 3 4 22). 7 ∙ 3 8 21 Answers: 19). 1/8 20). 1/1 = 1 21). ½ 22). 1/8

Keep Flip Change Dividing Fractions Keep the first fraction the same Flip the second fraction Change the sign of division to a multiplication sign Keep Flip Change Multiply the numerators together and the denominators together Then write your answer in lowest terms A ÷ C = A ∙ D B D B ∙ C B and C cannot equal zero.

Answers: 23). 6/7 24). 7/6 25). 15 26). 2/3 Example: Page 21 #23-26 23). 1 ÷ 7 = 2 12 24). 7 ÷ 1 12 2 25). 3 ÷ 1 4 20 26). 3 ÷ 9 5 10

Add/Subtract with the Same Denominator A + C = A+C B B B A - C = A-C Add/Subtract the numerators only Leave the denominator alone Write your answer in lowest terms 6+ 10 = 6 + 10 = 16 7 7 7 7 15 - 11 = 15-11= 4 = 1 16 16 16 16 4

Example 4 – 1 5 5 17 + 18 40 40 Answers 3 5 35 = 7 40 8

Equivalent Fractions Fractions with different numerators and denominators, but are equal in value. Example: 1 = 2 = 3 = 4 = 18 2 4 6 8 36 First think what number multiplied to the denominator will give you your new denominator Second multiply the numerator and denominator by that same number. Do not write in lowest terms

5 with a denominator of 21 7 Think : 7 times what number is 21? 3 Multiply the numerator and denominator by 3 5 ∙ 3 = 3 Does not change the value of the fraction! Why? 3 Is the same as one!

Write Each fraction as an equivalent fraction 1). 7 8 with a denominator of 64 2). 16 11 with a denominator of 33 3). 5 9 with a denominator of 72 1). 56/64 2). 48/33 3). 40/72

Add/Subtract with the Different Denominators Decide what is the common denominator between the two denominators Write each one as an equivalent fraction using the common denominator Add or subtract the numerators Leave the denominator alone Write your answer in lowest terms 5 + 1 12 8 Common Denominator: 24 5 ∙ 2 = 10 12 2 24 1 ∙ 3 = 3 8 3 24 10 + 3 = 13 24 24 24

Examples: 3 + 1 6 1 + 2 9 7 - 8 10 15 Answers: 23 30 5 9 1 6

Mixed Numbers to Improper Fractions To write a Mixed number into an improper fraction Multiply the Whole number by the denominator Add the numerator to your product Write your answer over the denominator Simplify if possible Example: 5 ⅞ (5)(8) = 40 40 + 7 = 47 Answer: 47 8

Whole Numbers to Fractions When you write a whole number as a fraction, you put your whole number over one. Example: 16 = 16 1