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.

12 1 x 12

2 x 63 x 44 x 3

Factors of 12:

1, 2, 3, 4, 6,12

421 x 422 x 213 x 144 x ??5 x ??6 x 77 x 6

Factors of 42:

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

Common Factors: 1, 2, 3, 6

Greatest Common Factor: 6

Example

What is the GCF of 18 and 27?

18 271 x 182 x 93 x 6

4 x ?5 x ?

6 x 3

Factors of 18:

1, 2, 3, 6, 9, 181 x 272 x ?3 x 94 x ?5 x ?6 x ?7 x ?8 x ?9 x 3

Factors of 27:

1, 3, 9, 27

Common Factors: 1, 3, 9

GCF: 9

What is the GCF of 48 and 60?

48 601 x 482 x 243 x 164 x 126 x 8

1 x 602 x 303 x 204 x 155 x 126 x 10

Factors of 48:

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

Factors of 60:

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

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

10, 20, 30, 40, 50, 60, 70, 80If you don’t see a common multiple, make each list go further.

81, 90, 99

90, 100, 110

The LCM of 9 and 10 is 90

Example 3:Find the LCM of 4 and 12

4, 8, 12, 16

12, 24, 36Answer: 12

Example 4:Find the LCM of 6 and 20

6, 12, 18, 24, 30, 36

20, 40, 60, 80, 100, 120

42, 48, 54, 60

Answer: 60

What are Fractions?

• Parts of a whole.

• Numbers between two whole numbers

2

1Example

4

13

Parts of a Fraction

4

1

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

Numerator: The PART how many of the whole we have

Mixed Numbers and Improper Fractions

Proper Fraction

• a numerator that is less than its denominator.

• Value is between 0 and 1

• Ex.

4

3

Improper Fraction

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

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

• Ex.

3

4

Mixed Number

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

• Ex.

4

32

Writing Mixed Numbers as Improper Fractions

1. Multiply denominator by whole number.

2. Add the product and the numerator.

3. The resulting sum = numerator of the improper fraction.

4. The denominator stays the same.

Example

24 3143

Writing Improper Fractions as Mixed Numbers

1. divide the denominator into the numerator.

2. quotient = whole number

3. remainder = numerator of the fraction.

4. divisor = denominator of the fraction.

Example

135 135

2

10 3

whole number

denominatornumerator

2 35

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

24

= 48

Equivalent Fractions

Creating Equivalent Fractions

• Multiply the numerator and denominator by the same number.

35

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

x 2x 2 =

610

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

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

35

28Factors of 28

1 282 144 7

Factors of 35 1 355 7

Divide by a common factor.

÷ 7

÷ 7 5

4Is the same as

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:

45

211

38

Writing Fractions in Simplest Form.

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

2. Divide both numbers by the GCF.

Example:

2028

201 x 20

2 x 10

4 x 5

281 x 28

2 x 14

4 x 7

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

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

Common Factors: 1, 2, 4

GCF: 4

We will divide by 4.

÷ 4÷ 4

= 57

Simplest Form

Comparing and Ordering Fractions

Strategy

1. Must make denominators the same.

2. Compare the numerators.

Writing Equivalent Fractions

Easy way

56

34 6 x 4 = 24

24 24

x 4

20x 6

18

20 > 18

>

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

• Find the LCM of both denominators.

712

599, 18, 27, 36, 45

12, 24, 36, 48, 60

36 36

x 4 20x 3

21

20 < 21

<

Another way

Ordering Fractions

1. Find the LCM of the denominators.

2. Use the LCM to write equivalent fractions.

3. Put the fractions in order using the numerators.

Example - Order from Least to Greatest:

3 2 18 5 4

8, 16, 24, 32, 40, 48

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

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

40 40 40

x 5 15x 8

16 x 1010

1/4 < 3/8 < 2/5