Download 4.5 Study Guide

4.5 Study Guide
Adding and Subtracting Fractions and Decimals
Learning Goals
4.5
a) determine common multiples and factors, including least common multiple and greatest common factor;
b) add and subtract fractions having like and unlike denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify
the resulting fractions, using common multiples and factors;
c) add and subtract with decimals; and
d) solve single-step and multistep practical problems involving addition and subtraction with fractions and with decimals.
Vocabulary
Multiple - A number that can be divided by another number without a remainder:
Factor - The numbers you multiply together to get another number
Greatest Common Factor - The largest number that divides evenly into two or more numbers.
Least Common Multiple – the smallest common multiple of the denominators of two or more
fractions (also known as the Least Common Denominator)
Simplest Form – A fraction whose numerator and denominator have no common factor greater than one
Examples and Explanations
The Greatest Common Factor (GCF) of two numbers is found by writing all the factors of each number and
determining the largest common factor.
8
12
The GCF of 8 and 12 is 4.
1,2,4,8
1,2,3,4,6,12
The Least Common Multiple (LCM) of two numbers if found by recording all of the multiples of each number and
determining the smallest common multiple. This is also referred to as the Least Common Denominator (LCD).
The LCM/LCD of 4 and 6 is 12.
4
6
8 12
12 18
16 24
When adding or subtracting like fractions, only the numerator changes. The denominator stays the same.
2
1 3
4 + 4= 4
3 2
1
4 - 4 = 4
When adding or subtracting unlike fractions, you must first find a common denominator by finding the LCD.
Then, multiply each fraction to find an equivalent fraction.
1 x2
2
=
6
3 x2
3
1 x3
+ x3 =
2
6
5
6
2
3
4 6
6 9
8 12
LCD = 6
All answers must be in Simplest Form.
Step 1: Improper fractions must be converted to mixed numbers (when appropriate)
Step 2: Find the GCF
Step 2: If the GCF is 2 or more, divide to reduce to lowest terms.
Example 1:
6
to simplest form
8
Reduce
Step 1: Skip – not improper Step 2: The GCF of 6 and 8 is 2
Example 2: Reduce
Step 3:
6 ÷2
8 ÷2
Final answer:
1
3
10
to simplest form
9
Step 1: Improper fraction. Use division to convert to a mixed number:
The remainder is written as a fraction = 1
10
is 10 ÷ 9.
9
1
9
Step 2: The GCF of 1 and 9 is 1, so it is already in simplest form. Final answer: 1
1
9
When adding and subtracting decimals, be sure to line up the decimal point. Fill in empty places with a
zero (0) if necessary.
3
7.4 - 3.39 =
-
10
7
.
4 0
3
.
3 9
4
.
0 1
Add the zero
here in order to
subtract.