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Fractions

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Fractions

A Review of the Basics

- Factors and Multiples

- 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

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

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

- 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.

- 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.

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

4, 8, 12, 16

12, 24, 36

Answer: 12

6, 12, 18, 24, 30, 36

42, 48, 54, 60

20, 40, 60, 80, 100, 120

Answer: 60

- Parts of a whole.
- Numbers between two whole numbers

Example

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.

- Multiply denominator by whole number.
- Add the product and the numerator.
- The resulting sum = numerator of the improper fraction.
- The denominator stays the same.

4

2

14

3

3

- divide the denominator into the numerator.
- quotient = whole number
- remainder = numerator of the fraction.
- divisor = denominator of the fraction.

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

- 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 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

- Find the greatest common factor (GCF) of the numerator and denominator.
- Divide both numbers by the GCF.

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

- Must make denominators the same.
- Compare the numerators.

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

- Find the LCM of the denominators.
- Use the LCM to write equivalent fractions.
- Put the fractions in order using the numerators.

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