Comparing and Ordering Fractions

Lesson 5-1

Least Common Multiple

a multiple of a number is the product of that number and any nonzero whole number.

LCM is the smallest multiple that they share (or have in common).

How to find the LCM

list the multiples of both numbers in ascending order until one multiple appears in both lists.

for larger numbers it’s faster to find the prime factors of each number. The LCM consists of all the factors that appear in either number raised to the greatest power that appears in any one of the numbers.

Find the LCM by listing multiples

Examples:

Multiples of 2:

Multiples of 4:

The number 4 is the least common multiple (LCM).

Multiples of 5:

Multiples of 6:

The number 30 is the least common multiple (LCM).

2, 4, 6, 8, …

4, 8, …

2, 4, 6, 8, …

4, 8, …

5, 10, 15, 20, 25, 30, 35, …

6, 12, 18, 24, 30, …

5, 10, 15, 20, 25, 30, 35, …

6, 12, 18, 24, 30, …

Try This

Find the LCM by listing multiples

3, 4 3: 3, 6, 9, 12, 15, …

4: 4, 8, 12, …

3: 3, 6, 9, 12, 15, …

4: 4, 8, 12, …

3, 4, 8 3: 3, 6, 9, 12, 15, 18, 21, 24, …

4: 4, 8, 12, 16, 20, 24, …

8: 8, 16, 24, …

3: 3, 6, 9, 12, 15, 18, 21, 24, …

4: 4, 8, 12, 16, 20, 24, …

8: 8, 16, 24, …

LCM is 12

LCM is 24

Find the LCM by using Prime Factorization

Examples:

To find LCM use the greatest power of each factor and

multiply.

40

12

52

32

3

2

1205323

LCM is 120

Try This

Find the LCM by using Prime Factorization

4216

326

6, 16

48324LCM

9, 15

5315

39 2

45532LCM

Try More

Find the LCM by using Prime Factorization

2

2

3218

5315

3212

12, 15, 18 ,6 2a

180532 22LCM

318a

323

22

3218

326

aa

aa

332 1832 aaLCM

Comparing Fractions

Examples: Graph and compare each pair of fractions.

is to the right of

0 1

,11

9

11

6

11

9

11

6

11

9,

11

6so >

11

9

11

6

is to the left of

-1 0

,2

1

10

1

10

1

2

1

2

1,

10

1so <

2

1

10

1

Try This

Examples: Graph and compare each pair of fractions.

0 1

,9

4

9

2

9

4

9

2

9

4

9

2>

,9

4

9

4<

-1 09

4

9

29

2

9

2

rewrite the fractions with a common denominator

then compare the numerators

the least common denominator (LCD) of two or more fractions is the LCM of the denominators.

Comparing Fractions with different denominators

Comparing Fractions with different denominators

,8

5Example:

10

7

Step 1: Find the LCM of 8 and 10328 5210

LCM = 40523

Step 2: Write equivalent fractions with a

denominator of 40.

,40

25

5

5

8

5

40

28

4

4

10

7

Step 3: Compare the fractions

40

25< ,

40

28so

8

5<

10

7

Try this

Compare each pair of fractions.

,7

6

5

4 717 515LCM = 3557

,35

30

5

5

7

6

35

28

7

7

5

4

LCM = 12322

,12

8

4

4

3

2

12

9

3

3

4

3

,3

2

4

3 313 224

7

6

5

4>

<

3

2

4

3