Fractions
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Fractions. A Review of the Basics. But First…We Remind You of…. Factors and Multiples. What are Factors. Numbers that multiply together to make our “given” number. Greatest Common Factor (GCF). The greatest common factor is the largest factor that two numbers share. Example. 12. 42.

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Fractions

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Fractions

A Review of the Basics


But First…We Remind You of…

  • Factors and Multiples


What are Factors

  • Numbers that multiply together to make our “given” number

Greatest Common Factor (GCF)

  • The greatest common factor is the largest factor that two numbers share.


Example

12

42

1 x 12

1 x 42

Factors of 12:

1, 2, 3, 4, 6,12

2 x 21

2 x 6

3 x 14

3 x 4

4 x ??

4 x 3

Factors of 42:

1, 2, 3, 6, 7, 14, 21, 42

5 x ??

6 x 7

7 x 6

Common Factors: 1, 2, 3, 6

Greatest Common Factor: 6


What is the GCF of 18 and 27?

18

27

Factors of 18:

1, 2, 3, 6, 9, 18

1 x 18

1 x 27

2 x ?

2 x 9

3 x 9

3 x 6

Factors of 27:

1, 3, 9, 27

4 x ?

5 x ?

4 x ?

6 x ?

5 x ?

7 x ?

Common Factors: 1, 3, 9

8 x ?

6 x 3

9 x 3

GCF: 9


What is the GCF of 48 and 60?

Factors of 48:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

48

60

1 x 48

1 x 60

2 x 30

2 x 24

3 x 20

3 x 16

4 x 15

Factors of 60:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

4 x 12

5 x 12

6 x 8

6 x 10

Common Factors: 1, 2, 3, 4, 6, 12

GCF: 12


What are Multiples

  • A multiple is formed by multiplying a given number by the counting numbers. Ex. “x” by 1, 2, 3, 4, 5, 6 etc.

Least Common Multiple (LCM)

  • the smallest number that is common between two lists of multiples.


EXAMPLE: Find the LCM of 12 and 18

  • The multiples of 12:

  • 12 x 1 = 12

  • 12 x 2 =24

  • 12 x 3 = 36

  • 12 x 4 = 48

  • 12 x 5 =60

  • The multiples of 18:

  • 18 x 1 = 18

  • 18 x 2 = 36

  • 18 x 3 = 54

  • 18 x 4 = 72

  • 18 x 5 = 90


12, 24, 36, 48, 60

18, 36, 54, 72, 90

The first number you see in both lists is 36.

The least common multiple of 12 and 18 is 36.


Example 2: Find the LCM of 9 and 10

9, 18, 27, 36, 45, 54, 63, 72

81, 90, 99

10, 20, 30, 40, 50, 60, 70, 80

90, 100, 110

If you don’t see a common multiple, make each list go further.

The LCM of 9 and 10 is 90


Example 3:Find the LCM of 4 and 12

4, 8, 12, 16

12, 24, 36

Answer: 12


Example 4:Find the LCM of 6 and 20

6, 12, 18, 24, 30, 36

42, 48, 54, 60

20, 40, 60, 80, 100, 120

Answer: 60


What are Fractions?

  • Parts of a whole.

  • Numbers between two whole numbers

Example


Parts of a Fraction

Numerator:

The PART how many of the whole we have

Denominator:

The WHOLE  how many pieces the whole has been broken into.


Mixed Numbers and Improper Fractions


  • Proper Fraction

  • a numerator that is less than its denominator.

  • Value is between 0 and 1

  • Ex.


  • Improper Fraction

  • Numerator that is more than or equal to its denominator.

  • Value is greater than 1 or less than -1.

  • Ex.


  • Mixed Number

  • shows the sum of a whole number and a proper fraction.

  • Ex.


Writing Mixed Numbers as Improper Fractions

  • Multiply denominator by whole number.

  • Add the product and the numerator.

  • The resulting sum = numerator of the improper fraction.

  • The denominator stays the same.


Example

4

2

14

3

3


Writing Improper Fractions as Mixed Numbers

  • divide the denominator into the numerator.

  • quotient = whole number

  • remainder = numerator of the fraction.

  • divisor = denominator of the fraction.


Example

2

whole number

13

5

13

5

10

3

numerator

denominator

3

2

5


Equivalent Fractions

Fractions that are the same amount, but with different numerators and denominators.

2

4

=

8

4


Creating Equivalent Fractions

  • Multiply the numerator and denominator by the same number.

We can choose any number to multiply by. Let’s multiply by 2.

3

x 2

6

So, 3/5 is equivalent to 6/10.

=

x 2

10

5


If you have larger numbers, divide the numerator and denominator by the same number.

÷ 7

Divide by a common factor.

Is the same as

Factors of 28

1 28

2 14

4 7

Factors of 35

1 35

5 7

÷ 7


Fractions in Simplest Form

Fractions are in simplest form when the numerator and denominator do not have any common factors besides 1.

Examples of fractions that are in simplest form:

4

2

3

8

5

11


Writing Fractions in Simplest Form.

  • Find the greatest common factor (GCF) of the numerator and denominator.

  • Divide both numbers by the GCF.


Example:

5

20

÷ 4

=

Simplest Form

7

÷ 4

28

20: 1, 2, 4, 5, 10, 20

20

28

28: 1, 2, 4, 7, 14, 28

1 x 20

2 x 10

4 x 5

1 x 28

2 x 14

4 x 7

Common Factors: 1, 2, 4

GCF: 4

We will divide by 4.


Comparing and Ordering Fractions


Strategy

  • Must make denominators the same.

  • Compare the numerators.


Writing Equivalent Fractions

Easy way

  • Find a common denominator is to multiply the two original denominators.

5

3

>

4

6

6 x 4 = 24

20 > 18

x 4

x 6

18

20

24

24


Another way

  • Find the LCM of both denominators.

7

5

<

9, 18, 27, 36, 45

9

12

12, 24, 36, 48, 60

20 < 21

x 3

x 4

20

21

36

36


Ordering Fractions

  • Find the LCM of the denominators.

  • Use the LCM to write equivalent fractions.

  • Put the fractions in order using the numerators.


Example - Order from Least to Greatest:

3

2

1

5

8

4

x 8

x 5

x 10

15

16

10

40

40

40

8, 16, 24, 32, 40, 48

1/4 < 3/8 < 2/5

5, 10, 15, 20, 25, 30, 35, 40

4, 8, 12, 16, 20, 24, 28, 32, 36, 40


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