Download 5.6 LCM.notebook

5.6 LCM.notebook
December 03, 2012
5­6 Using the Least Common Multiple (LCM)
Finding Multiples & Factors
Warm­up 12/4/12
IAN pg. 100
Write each fraction in simplest form.
1. 8 24
2. 100 40
3. 15x2 4. 17abc4
18xy
a3b
IAN pg. 101
Multiple ­ of a number is the product of that number and any other nonzero number.
Ex. Multiples of 3: 3, 6, 9, 12, 15, 18 ... Finding the Least Common Multiple (LCM)
LCM is the least multiple common to both numbers.
Ex. LCM of 6 and 9
Method 1: Listing multiples
Step 1: List multiples of each number.
Multiples of 6:
Multiples of 9:
Step 2: Identify the least common multiple for both.
IAN pg. 101
Method 2: Prime Factorization
Example: Find the LCM for 12, 30, 84
Step 1: Write the prime factorization for each number.
12
30
84
You Try:
IAN pg. 100
Find the LCM for each set of numbers.
1. 7, 21, 84
2. 9, 12, 15 3. 21, 28 Step 2: Circle all common factors and multiply all factors, but common factors only once.
12: 2 · 2 · 3
2 · 2 · 3 · 5 · 7 = 30: 2 · 3 · 5
84: 2 · 2 · 3 · 7
Finding the LCM of Monomials
IAN pg. 101
Example : 12a2b and 8ac
You Try:
Find the LCM.
1. 6c, 8cd
IAN pg. 100
2. 7y, 12y
3. 3t, 5t2,15
Use same method. Write Prime factorization of each.
12a2b
8ac
12a2b:
8ac:
1
5.6 LCM.notebook
December 03, 2012
Comparing Fractions
IAN pg. 101
Comparing Fractions with like numerators or denominators
* If denominator (bottom #) are the same then the numerator tells which is greater.
Example: 7 9 10 10
* If numerator (top #) of the fractions are the same the fraction with lesser denominator has greater value.
Example: 3 3 4 5
You Try:
IAN pg. 100
IAN pg. 101
Comparing Fractions ­ Unlike Denominators
& Numerators
Method 1 ­ LCD
Fractions with unlike denominators and numerators can be rewritten with LCD ­ Least Common Denominator.
The LCD is the LCM (least common multiple) of the denominators.
Example: 3 and 9 4 10
Step 1: Find the LCM of 4 and 10
Multiples of 4:
Multiples of 10:
Step 2: Write equivalent fractions with denominator of LCM.
3 4
9 10
Step 3: Compare the new numerators. Larger number is greater fraction.
IAN pg. 101
Method 2 ­ Cross Multiplication
Butterfly / Cross Bone Method
Compare using LCD.
1 and 2 6 8
Example: 3 9 4 10
Step 1: Cross Multiply opposite numerator and denominators. Write product above numerator.
Step 2: Compare products fraction with larger product above number is greater fraction.
Compare with Cross Multiplication.
According to the Humane Society, caring for a dogs costs an average of $7815 over 12 years. Caring for a cat costs $4723 over 15 years. 3 2 5 3
Which is more costly, caring for a cat or a dog?
Explain in fraction form
You Try:
IAN pg. 100
6 4 7 5
2
5.6 LCM.notebook
December 03, 2012
Homework: Workbook pg. 34 even
3