Learning Resources
Activity
Section 01 The Real Number System
- Classify each of the following numbers according to ALL the subsets of the real numbers to which it belongs, i.e. tell if the number is a natural number, a whole number, an integer, a rational number, an irrational number, a real number.
(a) 3 (b) -3 (c) 2.5 (d)
(e)
(f) 
(g) 
(h) 4.52
- John works at a local shoe store.
(a) What is the smallest number of pairs of shoes he can sell each week?
(b) Which set of numbers would describe the number of pairs sold?
(c) If x represents the number of pairs sold, combine your answers to (a) and (b) to write an inequality expressing the restriction on the number of pairs sold.
(d) John's boss feels that John could be selling more shoes, so he introduces a performance quota that states John must sell at least 20 pairs each week. Revise your inequality in (c) to reflect this new situation.
(e) John knows that based on his past experience he cannot expect to sell any more than 40 pairs, even in his best week. Revise your inequality in (d) to reflect this new situation. - Jane works at a men's clothing store. She gets paid $15 for each suit she sells.
(a) What set of numbers can be used to describe the number of suits she can sell?
(b) The store requires her to sell a minimum of 4 and limits her sales to a maximum of 20 suits per week. If n represents the number of suits she sells, write a sentence and a mathematical inequality to describe the number of suits Jane can sell each week.
(c) If y represents the amount of money she earns on suit sales, write a sentence and an inequality showing the range of the amount of money she can earn on the suit sales. - Which of the following inequalities are equivalent?
(a) x ³ 9 where x Î W; x > 8 where x Î W
(b) x ³ 5 where x Î W; x ³ 5 where x Î I
(c) x ³ 7 where x Î W; x ³ 7 where x Î R
(d) x £ 5 where x Î W; x £ 5 where x Î I
Section 02 Working with Fractions
Do as many of the following problems as you can mentally. You may use pencil and paper if necessary, but do not use a calculator.
- Reduce to lowest terms:
- Find the LCD of the following fractions:
- Convert to a mixed number:
- Convert to an improper fraction:
- Perform the indicated operations:
- Add:
- Simplify:
- If x =
and y = 
, evaluate 
Section 03 Working with Decimals and Percents
1. Perform the following calculations mentally.
(a) -0.3 x 0.15 (b) -4.8 ¸ 0.8
2. Round the following numbers as indicated:
(a) 3.467 to the nearest tenth.
(b) 0.03457 to the nearest thousandth.
(c) 57935 to the nearest ten.
3. Convert each of the following as indicated. Do whatever you can mentally
and use pencil and paper for the rest. Do not use a calculator.
(a) 
and 
to decimals.
(b) 1.45 and 0.275 to fractions.
(c) 22% to a decimal and a fraction.
4. (a) 20%x + 6 = 15
(b) x% of 10 + x% of 15 = 10.5
5. A person has a job which pays a base wage of $350 per week plus 2% commission on all sales. If the person received a check showing a gross amount of $399, what were his total sales for the week?
Section 04 Order of Operations
1. Simplify the following. Do as many as possible mentally and do not use a calculator:
(a) 
(b) 
(c) 
(d) 2 - (3 - x)2 (e) 3[2(x - 1)(x + 2)] (f) 
(g) 
2. If x = 
, evaluate (1 - x2) ¸ x2 + 1
Test Yourself
Print off a copy of the following Unit Test and put it in your Math 3103 binder. Then answer the questions in your binder.
1. Classify each of the numbers below according to ALL the subsets of the real
numbers to which it belongs:
(a) 
(b) 
(c) 
(d) 
2. Examine the two graphs below and then answer (a) to (d) for both:
Graph 1 Graph 2
(a) What is the smallest x-coordinate on each graph?
(b) What is the largest x-coordinate on each graph?
(c) Can the x-coordinate be any real number between these values in Graph 1? in Graph 2?
(d) Write one inequality which summarizes your answer in (a), (b), and (c). That is, state the domain of the relation shown in each graph.
(e) Repeat (a) - (c) for the y-coordinate and then state the range of the relation shown in each graph.
3. Put the following numbers in order from smallest to largest:
4. Perform the indicated operations. 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) 
(c) 
(d) 
(e) 
(f) 
(g) 
(h) 
6. Start with the number 16 (call it step 0). Take 
of this number (call it
step 1). Then take of the result in step 1 (call it step 2); then of the
result in step 2 (call it step 3); etc. Leave all answers in fractional form.
(a) Plot the points on a graph using the step numbers as the x-coordinate
and the results of your calculations as the y-coordinate.
(b) Describe the shape of the graph.
(c) Will the graph ever intersect or go below the x-axis? Explain.
7. (a) Express 0.532 as a fraction in lowest terms.
(b) Express 
as a percent.
8. (a) Solve for x:
(i) 75% of x = 0.32 (ii) x% of 19.2 = 11.52
(b) Joan bought a new car for $21 000. After one year it was worth $16 800, after two years it was worth $13 440
(i) What is the annual rate of depreciation?
(i) If she sells the car after five years, what should be the asking price?