Fractions
This presentation is the property of its rightful owner.
Sponsored Links
1 / 130

Fractions!! PowerPoint PPT Presentation


  • 88 Views
  • Uploaded on
  • Presentation posted in: General

Fractions!!. Prime Numbers and Factorization. How many positive prime numbers are less than 100?. Answer: 25. What is the sum of the prime numbers between π and 10 π ?. Answer: 155. List the positive prime numbers less than 100 that have the units digit equal to 3.

Download Presentation

Fractions!!

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Fractions

Fractions!!


Prime numbers and factorization

Prime NumbersandFactorization


Fractions

How many positive prime numbers are less than 100?


Answer 25

Answer:25


Fractions

What is the sum of the prime numbers between π and 10π?


Answer 155

Answer:155


Fractions

List the positive prime numbers less than 100 that have the units digit equal to 3.


Answer 3 13 23 43 53 73 83

Answer:3, 13, 23, 43, 53, 73, 83


Prime factorization

Prime Factorization


Fractions

Factoring is like taking a number apart. It means to express a number as the product of its factors. Factors are either composite numbers or prime numbers (except that 0 and 1 are neither prime nor composite).The number 12 is a multiple of 3, because it can be divided evenly by 3.3 · 4 = 123 and 4 are both factors of 123 · 2 · 2 (prime factorization of 12)12 is a multiple of both 3 and 4.


Fractions

Write the prime factorization of:

100


Answer 2 2 5 5 or 2 5 prime power factorization

Answer:2∙2∙5∙5or2² ∙ 5²(Prime-Power Factorization)


Fractions

Write the prime factorization of:

972


Answer 2 2 3 3 3 3 3 or 2 3 prime power factorization

Answer:2∙2∙3∙3∙3∙3∙3 or2² ∙ 3⁵(Prime-Power Factorization)


Fractions

List the prime factorization of the following terms (includes variables):

25n²


Answer 5 5 n n

Answer:5·5·n·n


Fractions

List the prime factorization of the following terms (includes variables):

92xy


Answer 2 2 23 x y

Answer:2·2·23·x·y


Factors

Factors


Fractions

List all the positive factors of

30


Answer 1 2 3 5 6 10 15 30

Answer:1, 2, 3, 5, 6, 10, 15, 30


Fractions

List all the positive factors of

87


Answer 1 3 29 87

Answer:1, 3, 29, 87


Greatest common factor gcf

Greatest Common Factor (GCF)


Fractions

Greatest Common FactorThe highest number that divides exactly into two or more numbers. If you find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.Abbreviated "GCF". Also called "Highest Common Factor"Example: the GCF of 12 and 30 is 6, because 1, 2, 3 and 6 are factors of both 12 and 30, and 6 is the greatest.


Fractions

Find the GCF of

24 & 28


Answer 4

Answer:4


Fractions

Find the GCF of

39v & 30uv


Answer 3v

Answer:3v


Fractions

Find the GCF of

35n²m & 21m²n


Answer 7nm

Answer:7nm


Fractions

Find the GCF of

36xy³ & 24y²


Answer 12y

Answer:12y²


Fractions

Find the GCF of

105x, 30yx & 75x


Answer 15x

Answer:15x


Least common multiple lcm

Least Common Multiple (LCM)


Fractions

Least Common MultipleThe smallest (non-zero) number that is a multiple of two or more numbers.Least Common Multiple is made up of the words Least, Common and Multiple:What is a "Multiple" ?The multiples of a number are what you get when you multiply it by other numbers (such as if you multiply it by 1,2,3,4,5, etc). Just like the multiplication table. Here are some examples: The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, etc ... The multiples of 12 are: 12, 24, 36, 48, 60, 72, etc... What is a "Common Multiple" ?When you list the multiples of two (or more) numbers, and find the same value in both lists, then that is a common multiple of those numbers. For example, when you write down the multiples of 4 and 5, the common multiples are those that are found in both lists:The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,... The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...Notice that 20 and 40 appear in both lists? So, the common multiples of 4 and 5 are: 20, 40, (and 60, 80, etc ..., too) What is the "Least Common Multiple" ?It is simply the smallest of the common multiples. In our previous example, the smallest of the common multiples is 20 ...... so the Least Common Multiple of 4 and 5 is 20.


Fractions

Finding the Least Common MultipleIt is a really easy thing to do. Just start listing the multiples of the numbers until you get a match.Example: Find the least common multiple for 3 and 5:The multiples of 3 are 3, 6, 9, 12, 15, ..., and the multiples of 5 are 5, 10, 15, 20, ..., like this:As you can see on this number line, the first time the multiples match up is 15. Answer: 15More than 2 NumbersYou can also find the least common multiple of 3 (or more) numbers.Example: Find the least common multiple for 4, 6, and 8Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...Multiples of 6 are: 6, 12, 18, 24, 30, 36, ...Multiples of 8 are: 8, 16, 24, 32, 40, ....So, 24 is the least common multiple (I can't find a smaller one !)


Fractions

Find the LCM of

35 & 25


Answer 175

Answer:175


Fractions

Find the LCM of

30, 25 & 10


Answer 150

Answer:150


Fractions

Find the LCM of

18 & 6v


Answer 18v

Answer:18v


Fractions

Find the LCM of

3x² & 10


Answer 30x

Answer:30x²


Fractions

Find the LCM of

20y & 14y²


Answer 140y

Answer:140y²


Fractions

Find the LCM of

16x²y & 32x


Answer 32x y

Answer:32x²y


Fractions

Find the LCM of

8y², 16xy & 16y


Answer 16y x

Answer:16y²x


Fractions

What is the negative difference of the least common multiple (LCM) and the greatest common factor (GCF) of:

80, 140, and 200


Answer 2780

Answer:-2780


Types of fractional numbers

Types of Fractional Numbers

  • A proper fraction is a fraction whose value is less than 1 (numerator < denominator)

  • An improper fraction is a fraction whose value is greater than or equal to 1 (numerator > denominator)

  • A mixed number is a number whose value is greater than 1 made up of a whole part and a fraction part


Improper fraction mixed number

Improper FractionMixed Number

  • Denominator: tells us how many parts make up a whole

  • Numerator: tells us how many parts we have

  • How many wholes can we make out of the parts we have?

  • Divide the numerator by the denominator  the quotient is the whole part

  • How many parts do we have remaining?

  • The remainder (over the denominator) makes up the fraction part


Simplest form of a fraction

Simplest Form of a Fraction

  • A fraction is in simplest form when there are no common factors in the numerator and the denominator.


Ex simplest form

Ex: Simplest Form

Ex: 6/8 and 3/4 are equivalent

The fraction 6/8 is written in simplest form as 3/4

=

=

=

1 x

Magic one


Ex write 12 42 in simplest form

Ex: Write 12/42 in simplest form

  • First prime factor the numerator and the denominator:

  • 12 = 2 x 2 x 3 and 42 = 2 x 3 x 7

  • Look for Magic Ones

  • Simplify

=

=

=

1 x 1 x

=

Notice: 2 x 3 = 6 = GCF(12, 42)

 factoring (dividing) out the GCF will simplify the fraction


Ex write 7 28 in simplest form

Ex: Write 7/28 in simplest form

  • What is the GCF(7, 28)?

    • Hint: prime factor 7 = 7

    • prime factor 28 = 2 x 2 x 7

= 7

=

=

=

1 x

=

Dividing out the GCF from the numerator and denominator simplifies the fraction.


Ex write 27 56 in simplest form

Ex: Write 27/56 in simplest form

  • What is the GCF(27, 56)?

    • Hint: prime factor 27 = 3 x 3 x 3

    • prime factor 56 = 2 x 2 x 2 x 7

= 1

There is no common factor to the numerator and denominator (other than 1)

Therefore, 27/56 is in simplest form.


Fractions

Rational and Irrational Numbers


Fractions

Rational and Irrational Numbers Essential Question

How do I distinguish between rational and irrational numbers?


Fractions

Real Numbers

Rational numbers

Irrational numbers

Integers

Whole

numbers

The set of real numbers is all numbers that can be written on a number line. It consists of the set of rational numbers and the set of irrational numbers.


Fractions

Rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals.

⅔, ⅕, ¼ or

144 = 12


Fractions

Caution!

A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.

Irrational numberscan be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, the square root of 2 is not a perfect square, so the square root of 2 is irrational. Also, π is irrational.


Fractions

Make a Venn Diagram that displays the following sets of numbers:

Reals, Rationals, Irrationals, Integers, Wholes, and Naturals.

Reals

Rationals

-2.65

Integers

-3

-19

Wholes

0

Irrationals

Naturals

1, 2, 3...


Fractions

Classifying Real Numbers

Write all classifications that apply to each number.

A.

5 is a whole number that is not a perfect square.

5

irrational, real

B.

–12.75

–12.75 is a terminating decimal.

rational, real

16

C.

whole, integer, rational, real


Fractions

9 = 3

Write all classifications that apply to each number.

9

A.

whole, integer, rational, real

–35.9

–35.9 is a terminating decimal.

B.

rational, real

81

C.

whole, integer, rational, real


Fractions

A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all.


Adding and subtracting fractions

Adding and SubtractingFractions


Evaluate the expression 6

Evaluate the expression:6- ¹⁄₆


Answer

Answer:³⁵/₆


Evaluate the expression

Evaluate the expression:⅕+ ¾


Answer1

Answer:¹⁹/₂₀


Evaluate the expression 4 5 7 8

Evaluate the expression:(-4/5) – 7/8


Answer2

Answer:- ⁶⁷/₄₀


Evaluate the expression 10 7 1 6

Evaluate the expression:(-10/7) + 1/6


Answer3

Answer:- ⁵³/₄₂


Evaluate the expression 2

Evaluate the expression:2 – ¹³/₈


Answer 3 8

Answer:3/8


Evaluate the expression 4 3 3 2

Evaluate the expression:(-4/3) – (-3/2)


Answer 1 6

Answer:1/6


Evaluate the expression 3 4

Evaluate the expression:- 3 ⅗ - 4 ⅖


Answer 8

Answer:-8


Evaluate the expression 2 1

Evaluate the expression:(-2⁷/₈) + (-1 ¹/₂)


Answer 41

Answer: -4 ³/₈


Evaluate the expression 2 11

Evaluate the expression:(-2⁵/₆) - (-1 ¹/₄)


Answer 1

Answer: -1 ⁷/₁₂


Evaluate the expression 21

Evaluate the expression:2⁴/₅ - ⁵/₈


Answer 2

Answer: 2 ⁷/₄₀


Multiplying fractions

Multiplying Fractions


Evaluate the expression1

Evaluate the expression:-⁵/₄ · ¹/₃


Answer4

Answer: -⁵/₁₂


Evaluate the expression 22

Evaluate the expression:-2 · ³/₇


Answer5

Answer: -⁶/₇


Dividing fractions

Dividing Fractions


Evaluate the expression2

Evaluate the expression:- ¹/₅ ÷ ⁷/₄


Answer6

Answer: - ⁴/₃₅


Evaluate the expression3

Evaluate the expression:- ¹/₂ ÷ ⁵/₄


Answer7

Answer: - ²/₅


Evaluate the expression4

Evaluate the expression:- ³/₂ ÷ ⁻¹⁰/₇


Answer8

Answer: ²¹/₂₀


Evaluate the expression 23

Evaluate the expression:- ⁹/₅ ÷ 2


Answer9

Answer: -⁹/₁₀


Multiplying and dividing mixed numbers

Multiplying and DividingMixed Numbers


Evaluate the expression 2 4

Evaluate the expression:-2²/₃ · 4 ¹/₁₀


Answer 10

Answer:-10 ¹⁴/₁₅


Evaluate the expression 2 12

Evaluate the expression:-2 ¹/₅ · (-1 ³/₄)


Answer 3

Answer: 3 ¹⁷/₂₀


Evaluate the expression 2 3

Evaluate the expression:-2 ÷ (-3 ⁴/₅)


Answer10

Answer:+ ¹⁰/₁₉


Evaluate the expression 3 2

Evaluate the expression:- 3 ⁷/₁₀ ÷ 2 ¹/₄


Answer 11

Answer:-1 ²⁹/₄₅


Fractions

Challenge Problems


3 3 2 3 2

3_________ 3___ 2 + 3/2

2 +

2 +


Answer 31

Answer:3 ¹/₂₀


Fractions

Simplify completely:

4x²y

2x


Answer 2xy

Answer:2xy


Fractions

Simplify completely:

y¯¹

y¯²


Answer y

Answer:y


Fractions

Simplify completely:

16x⁴y¯¹

4x²y¯²


Answer 4x y

Answer:4x²y


Fractions

Simplify completely:

36x³y⁶z¹²

4x¯¹y³z¹⁰


Answer 9x y z

Answer:9x⁴y³z²


Fractions

Simplify completely:

21x³y⁷z¹⁴30x³z¯⁵

18x⁴y⁶ y¹²z¯⁶

·


Answer 35x z y

Answer:35x²z¹⁵y¹¹


  • Login