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• Before the bell rings...
– Have your covered textbook with you.
1. Solve. 0.073 + 10.1909 =
2. Compute. -350 x -7 =
• Before the bell rings...
– Have your covered textbook with you.
1. Solve. 0.073 + 10.1909 =
2. Compute. -350 x -7 =
10.2639
2,450
Essential Questions
1. What is the value of studying fractions?
2. What is the relationship between good number sense and working with fractions?
Comparing Fractions& Mixed Numbers
Section 4.5
P. 198 - 201
• In this section you will be using LCM (LCD) to compare fractions. (also a review)
• You will be working with fractions less than one and fractions greater than one (improper fractions and mixed numbers)
• This will test your understanding of the value of fractions.
• The least common multiple is the smallest non-zero common multiple (when comparing two or more numbers)
• List the multiples of 3
• List the multiples of 7
• Common multiples include:
• LCM is 21
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51, . .
7,14,21,28,35,42,,49, . . .
21, 42, 63, ???
• The least common multiple is the smallest non-zero common multiple (when comparing two or more numbers)
• List the multiples of 3
• List the multiples of 7
• Common multiples include:
• LCM is 21
• The LCM of any two prime numbers can be found by . . _______________________________
• Find the LCM for 11 and 7• 7 x 11=
• Find the LCM for 5 and 13• 5 x 13 =
multiplying the two numbers together
• The LCM of any two prime numbers can be found by . . _______________________________
• Find the LCM for 11 and 7• 7 x 11=
– 77
• Find the LCM for 5 and 13• 5 x 13 =
– 65
multiplying the two numbers together
• This is also true for numbers that are relatively prime.
• Find the LCM for 8 and 9– 8 x 9 =
• Find the LCM for 4 and 15– 4 x 15
• This is also true for numbers that are relatively prime.
• Find the LCM for 8 and 9– 8 x 9 =
• 72
• Find the LCM for 4 and 15– 4 x 15
• 60
• The division box is probably the easiest method to find LCM.
• Find the LCM for 45 and 50– LCM: 450
• Remember, divide common factors until the top numbers are relatively prime. (no common factors other than one)
• Use your divisibility rules to help you.
45 50
EXAMPLE 1 Comparing Fractions Using the LCD
Find the least common denominator of the fractions. The LCM of 8 and 12 is 24, so the least common denominator is 24.
STEP 1
STEP 2 Use the least common denominator to write equivalent fractions.
38
924=
512 = 10
24
Compare and .38
512
= 3 33 8 = 5 2
12 2
STEP 3 Compare the numerators:
9 < 10, so 924 < 10
24
ANSWER
3 8 <
512
GUIDED PRACTICE for Examples 1
Copy and complete the statement with < , > or =
1. 23
5 8
?
Find the least common denominator of the fractions. The LCM of 3 and 8 is 24, so the least common denominator is 24.
STEP 1
STEP 2 Use the least common denominator to write equivalent fractions.
23
1624=
5 8 = 15
24= 5 3 8 3= 2 8
3 8
STEP 3 Compare the numerators:
16 > 15, so 1624 > 15
24 >
ANSWER
2 3
5 8
GUIDED PRACTICE for Examples 1
Copy and complete the statement with < , > or =
2. 24
15 20
?
Find the least common denominator of the fractions. The LCM of 4 and 20 is 20, so the least common denominator is 20.
STEP 1
STEP 2 Use the least common denominator to write equivalent fractions.
24
1520= 2 5
4 51020=
STEP 3 Compare the numerators:
10 < 15, so 1020 < 15
20
ANSWER
2 4 <
1520
GUIDED PRACTICE for Examples 1
Copy and complete the statement with < , > or =
3. 310
2 4
? .
SOLUTION
Find the least common denominator of the fractions. The LCM of 10 and 4 is 20, so the least common denominator is 20.
STEP 1
STEP 2 Use the least common denominator to write equivalent fractions.
310
620=
2 4= 3 2
10 5= 2 5
4 5 = 1020
GUIDED PRACTICE Comparing Fractions Using the LCD
Copy and complete the statement with < , > or =
3. 310
2 4
? .
SOLUTION
6 < 10, so 620 < 10
20
Because , you can write
ANSWER
620
1020<
310 <
2 4
STEP 3 Compare the numerators:
EXAMPLE 3 Comparing Mixed Numbers
Write equivalent fractions using the LCD, 35.
STEP 1
Orangutans A female orangutan is about
373 is about2
53
feet tall. Which of the two orangutans is taller?
feet tall. A male
3
3 7 =
24 7 =
24 57 5 =
12035
3
2 5 =
17 5 = 17 7
5 7 =11935
STEP 2
Compare the fractions:
12035
>11935
,so 3 7
> 3
25 3
The female orangutan is taller.
ANSWER
GUIDED PRACTICE for Examples 2 and 3
Copy and complete the statement with <, >, or =.
5. 165
1 3
? . 3
Find the least common denominator of the fractions. The LCM of 5, and 3 is 15, so the LCD is 15.
STEP 1
Use the least common denominator to write equivalent fractions
STEP 2
= 10 5 3 53 1
3 =3 3 + 1
3 = 50
15
STEP 3 Compare the numerators:
48 < 50, so 4815 < 50
15ANSWER
165 < . 3
1 3
16 5
4815
== 16 35 3
GUIDED PRACTICE for Examples 2 and 3
8. Order the numbers , and from least to greatest.
2 79
2 512
114
Find the least common denominator of the fractions. The LCM of 9,12 and 4 is 36, so the LCD is 36.
STEP 1
Use the least common denominator to write equivalent fractions
STEP 2
2 7 9
= 25•4 9•4
2•9 + 7 9
= 10036
=
29•312•3=2 5
122•12+5
12 = = 87
36
11 4
= 11•9 4•9
= 99 36
Compare the numerators:STEP 3
87 < 99, 99 < 100
ANSWER
2 512
114
, and 2 79
• Classzone Activity
on ordering mixed and improper fractions
Check it out!
Homework
• P.200 #7-18 all
