Math 020- Fractions II
Least Common Multiple (LCM):
A multiple of a number is the product of that number and another natural number. For example the
multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and ….
Common multiples are multiples that are the same for 2 or more numbers. A common multiple for 3
and 5 is 15.
Finding the LCM for a list of numbers:
Method 1: Write a list of multiples for all numbers on the list, starting with the largest multiple.
Compare lists until a least common multiple is found.
Example: Find the the LCM for 8 and 10.
10: 10, 20, 30, 40, 50, 60, 70, 80, …
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, …
The common multiples for 8 and 10 we found so far are 40 and 80. The LCM is 40.
Practice: Find the LCM for the listed numbers.
1. 15 and 50
2. 12 and 18
3. 4 and 6
Method 2: Using Prime Factorization to find the LCM
1. Write the prime factorization for each number
2. For each different prime factor in step 1, circle the greatest number of times that factor occurs in any
one factorization.
3. The LCM is the product of the circled factors.
Example: Find the LCM for 72 and 60
72 = 2 * 2 * 2 * 3 * 3
60 = 2 * 2 * 3 * 5
Circle the greatest number of times a factor appears in either factorization.
Multiply the circled factors to find the LCM.
Practice: Find the LCM for the listed numbers:
1. 8, 6, 27
2. 34, 68
3. 48, 54
Adding and Subtracting Fractions:
In order to add or subtract fractions, the fractions must have a common denominator. If the fractions
have a common denominator, then just simply add or subtract numerators and place the answer over
the common denominator. Simplify if needed. If fractions do not have a common denominator, we
must find the least common denominator (LCD) for all fractions being added or subtracted.
Adding and Subtracting Fractions with a Common Denominator:
1.
=
2.
3.
Adding and Subtracting Fractions with Unlike Denominators:
1. Find the LCM of the denominators of the fractions. This number is the least common denominator
(LCD).
2. Write the fraction as an equivalent fraction whose denominator is the LCD.
3. Add or subtract the like fractions.
4. Write the sum or difference in simplest form.
Examples: Add or Subtract the Fractions
1.
2.
3.
Practice: 1.
2.
3.
Adding and Subtracting Mixed Numbers:
To add or subtract mixed numbers, add or subtract the fractions parts, then add or subtract the whole
number parts. Sometimes when subtracting mixed numbers, borrowing may be needed.
Examples:
1.
2.
3.
2.
3.
Practice:
1.
Comparing Fractions: To compare fractions, write the fractions with a common denominator. The
fraction with the larger numerator is the greater fraction.
Example: Insert < or > to make a true statement.
Practice:
1.
Order of Operations:
1. Perform all operations within grouping symbols first, starting with the innermost set.
2. Evaluate any expressions with exponents.
3. Multiply or Divide in order from left to right.
4. Add or subtract in order from left to right.
Practice:
1.
3.
5. [(
2.
( )
)
4. (
(
) =
)] =
Applications:
1. A carpenter cuts a piece
piece?
ft long from a cedar plank that is
ft long. How long is the remaining
2. There are 13 stripes of equal width in the flag. If the width of a flag is
ft, find the width of each
stripe.
3. Betty is building a bookcase. Each shelf will be
feet long, and she needs 7 shelves.
a. How many shelves can she cut from an 8-foot board?
b. How many 8- foot boards will she need to make the 7 shelves?
4. A small box measures 3 inches by
inches by 1 inch. Find the volume of the box. Remember that