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

• 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!

• 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!

1. 402. 633. 81

• Answers1. 40 = (2)(2)(2)(5)2. 63 = (7)(3)(3)3. 81 = (3)(3)(3)(3)

Writing Fractions in Lowest TermsUsing Product of Prime Numbers

1. 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)

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

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

ANSWER13

Examples:2035

2470

Writing Fractions in Lowest Termsby 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 FractionsA ∙ C = A∙CB D B∙DB 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∙¼20). 10 · 3

6 5

21). 2 · 3

3 4

22). 7 ∙ 3

8 21

Answers:

19). 1/820). 1/1 = 121). ½22). 1/8

Dividing Fractions

Keep FlipChange

Keep the first fraction the same

Flip the second fractionChange the sign of division to a

multiplication sign

A ÷ C = A ∙ DB D B ∙ CB and C cannot equal zero.

Multiply the numerators together and the denominators togetherThen write your answer in lowest terms

• Example: Page 21 #23-26

23). 1 ÷ 7 = 2 1224). 7 ÷ 1 12 225). 3 ÷ 1 4 2026). 3 ÷ 9 5 10

Answers:

23). 6/7

24). 7/6

25). 15

26). 2/3

Add/Subtract with the Same Denominator

A + C = A+CB B B

A - C = A-CB B B

Add/Subtract the numerators only

Leave the denominator alone

Write your answer in lowest terms

6+ 10 = 6 + 10 = 167 7 7 7

15 - 11 = 15-11= 4 = 116 16 16 16 4

• Example4 – 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 = 182 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?3Multiply the numerator and denominator by 35 ∙ 3 = 7 33 Does not change the value of the fraction! Why?33 Is the same as one!3

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 + 112 8Common Denominator: 24

5 ∙ 2 = 1012 2 24

1 ∙ 3 = 38 3 24

10 + 3 = 1324 24 24

Examples:3 + 15 6

1 + 2 3 9

7 - 810 15

Answers:2330

59

16

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) = 4040 + 7 = 47Answer: 47

8

Whole Numbers to Fractions

• When you write a whole number as a fraction, you put your whole number over one.

• Example: 16 = 161