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MATH 581- Hargrove
CHAPTER 3: Adding & Subtracting Fractions Study Guide
3.1, Adding & Subtracting Like Fractions
I. Adding Like Denominators
A.
B. Adding with the same denominator
- Add the _____________and find the ___________.
- Keep the same _________________.
- ________________, if possible.
C. Examples
I. Subtracting Like Denominators
A.
B. Subtracting with the same denominator
- Subtract the _____________and find the ________________.
- Keep the same _________________.
- ________________, if possible.
C. Examples
3.2, Least Common Multiples
I. Finding the LCM
A. The LCM of two whole numbers is the ___________ number that is divisible by_________
numbers.
B. Method I: Using lists of multiples
- List the multiples for both numbers.
- Locate the common multiples.
- The least common multiple is the smallest common multiple.
C. Examples
- Find the LCM for 20 & 30
- Find the LCM for 9 & 12
- Find her LCM for 12 & 15 4. Find the LCM for 6 & 8.
D. Three or more numbers
- Find the LCM for 10, 20, 50
- Find the LCM for 20, 40, 60
II. Method II: Using prime factorization.
A. Process:
- List the prime factorization for both numbers.
- Find the factors common to both & group together as a product of primes.
- Take the remaining factors & multiply them by the common factors to find the LCM.
B. Examples
1. 20 = ________________ 2. 9 = __________________
36 = ________________ 12 = _________________
LCM = ______________ LCM = _______________
II. A jogger ran
mile stopped to rest, and then ran another
mile. How far did he run?
III. Subtracting with Unlike Denominators
A. Process: just like adding with unlike denominators
B. Examples
Section 3.4, Adding & Subtracting Mixed Numerals
I. Addition
A. Process: Add all of the whole numbers. Add all of the fractions. Simplify.
B. Examples
II. Subtraction
A. Without borrowing
B. With Borrowing
III. Application
A. On two business days, a salesperson drove 144
miles and
miles.
How many miles were driven by the end of the trip?
B. The heaviest marine mammal in the world is the blue whale at
tons. The sixth heaviest
mammal is the humpback whale at
tons. Find the difference in their weights.
C. Multi-step problems: There are
gallons of water in a barrel.
Gallons are used for
watering plants and 8
gallons are added into the barrel due to run-off from the rain gutters.
How many gallons of water are in the barrel after these two events?
- Simplify.
2
5. Margin Exercises on pg. 226, #
a)
b)
c)
2
d)
2
