Learning Resources
Lesson
Addition and Subtraction Algorithms
To add or subtract two fractions, first find their LCD. Second, express both fractions as equivalent fractions with this denominator. Then simply add or subtract the numerators. This is shown in the example below:
Example 1
Perform the indicated operation: 
Solution
If the problem contains mixed numbers, one method of addition and subtraction is to first express the mixed numbers as improper fractions. Then proceed as in Example 1.
Example 2
Perform the indicated operation: 
Solution
We will deal with the addition and subtraction of fractions whose numerators and/or denominators contain algebraic expressions in more detail in Unit IV of this course. The following example will serve to show that the method applied to addition and subtraction of numerical fractions is directly applicable to algebraic fractions.
Example 3
Perform the indicated operation: 
Solution
Applications to Graphs
In earlier courses you learned how to generate graphs from a table of values. Usually the table contained integer values or decimals, but many patterns for graphs are generated using fractions as well. This is illustrated in the following example.
Example 1
The Sir Robert Bond Bridge over the Exploits River is 4 
metres above the normal water level. During a spring flood, the water began rising at the rate of 
m/h. Assume the water continued to rise at this rate to answer the following questions:
- Construct a table in which the independent variable is time and the distance of the water below the bridge is the dependent variable.
- Use this table to construct a graph of distance verses time.
- Can the points on the graph be connected? Explain.
- From the graph, read when the water reaches the bridge.
Solution
Activity
Print off a copy of this page and add it to your Math 3103 binder. Then answer the questions in your binder.
- Add or subtract as indicated. Do whatever problems you can mentally. Do the rest using pencil and paper. Do not use technology (calculators, etc.) to help you do these problems:
(a)
+ 
(b) 5 - 
(c) 
- 3 (d) 3 - 5
(e)
- 2
(f) 3
- 2
+ 1 (g) -7 + 3
- 6
(h) 4
- 
- 
(i) 
- 
(j) 
+ 
- Beth had $10 on day 0. Each successive day her dad gave her $
(a) Use a table to draw the graph of this data for the first ten days.
(b) What is the shape of the graph?
(c) Does it make sense to connect the points?
(d) What is the domain and range of the graph?
Test Yourself
- Add or subtract as indicated. You should be able to do these problems mentally.
(a)
(b) 
(c) 
(d) 
(e)
(f) 
- Add or subtract as indicated.
(a)
(b) 
(c) 
- Add or subtract as indicated.
(a)
(b) 
- A farmer sells hay in bundles each weighing
of a ton. He has 2tons of hay already sold (day = 0) and every day for the next week he sells an additional bundle.
(a) Use a table of values to graph the information in the problem.
(b) Does it make sense to connect the points on the graph? Explain.
(c) What is the domain and range of the graph?