UNIT 1
Numeracy Review
Topics Covered in this Unit Include: Integers, Fractions, and Percents
Evaluations Given this Unit (Record Your Marks Here)
Mastery Test #1 – IntegersMastery Test #2 – Rationals
Mastery Test #3 – Percents
Estimation Worksheet
1. Use rounding to estimate the results of:
a) 346 + 221 + 147b) 868 – 434c) 34.79 + 12.56 + 29.89 + 15.21
2. Use the clustering method of estimation to estimate the results of:
a) 56 + 44 + 59 + 51b) 18.45 + 20.56 + 22.99c) 387 + 415 + 390 + 406
3 Estimate each of the following:
a) 34.5 x 21.9b) 23.47 x 19c) 130 11
d) 63 x 0.89e) 137 x 1.873
4. Last month, Carl earned $157.39 in his part-time job and Susan earned $211.87 in her job.
Estimate the difference in their earnings.
5. Rachel bought three items for $2.45, $3.56 and $11.18. Estimate how much change she
would receive from a $20 bill.
Integers Worksheet #1
Replacing Double Signs Overview
When you have questions with double signs ex. (+2) – (- 4) or (-5) + (- 6) the rule for getting rid of the double signs is:
If both of the signs are the same, replace the two signs with a “+”.
Example: (+3) – (-5) + (+3) can be rewritten as 3 + 5 + 3 with all of the double signs removed
If the two signs are different, replace the two signs with a “ – “.
Example: (+3) + (-5) - (+3) can be rewritten as 3 - 5 - 3 with all of the double signs removed
Rewrite each of the following with all of the double signs removed and then find the value of the expression. Do NOT use calculators to do these questions.
1. 5 – (-3) + (-4)2. -6 + (-4) + (+7)3. (-9) + (-2) + (+4) – (+5)
4. 8 + (-7) + (-5)5. (-2) – (-5) + (-6)6. 4 + (-5) – (-10)
7. 3 – (+5) + (-6)8. 5 + 10 – (-4)9. (-5) – (-5) + 7 – (-3)
10. (-4) + (-7) – (-6) – (+10) 11. 3 – (-5) + (-2) – 412. (-4) + (+6) – (-4) + (-6)
Integers Worksheet #2
Do NOT use calculators for this sheet
Do your rough work here
Integers Worksheet #3
Do NOT use calculators for this sheet
Do your rough work here
Integers Worksheet #4
Do NOT use calculators for this sheet
1. (-3) x (+5)2. (-4)(-2)(-1)3. 5 x (-4) x 2
4. 6 x 4 x (-2)5. (5)(-1)(4)(-3)6. 8 x (-2) x (-3)
7. (-4)(-2)(0)(-9)8. (-10) x (-4) x (-2)9. (-1)(-2)(-3)(-4)(-5)
10. (-10) ÷ (-2)11. 16 ÷ (-4)12. (-81) ÷ (-9)
13. 14. 15.
Integers Worksheet #5
Do Not use a calculator.Remember to use BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, Subtraction) so that your answers are correct.
Integers Summary
Addition
When adding two numbers that have signs that are different, ignore the signs and subtract the smaller number from the larger. The sign of the answer will be the same as the sign of the integer with the largest number (after you ignore the signs)
ex. (-5) + (+12) ……. do 12 – 5 = 7
answer will be +7 since 12 is positive and 12 is larger than 5
(-8) + (+4) ……… 8 – 4 = 4
answer is -4
When adding two numbers that have signs that are the same add the numbers together and the answer will have the same sign as the numbers.
ex. (-10) + (-4) = -14 (numbers are negative so sign is negative and 10 + 4 = 14
Subtraction
When subtracting integers you add the opposite.
ex. (-4) – (-2) = (-4) + (+2) = -25 – (+10) = 5 + (-10) = -5
Replacing Double Signs
When two signs are written side by side you can replace them with a single sign that is negative if the two signs are different and positive if the two signs are the same
ex. (-3) + (-2) – (-8) – (+19) = -3 -2 + 8 – 19
Multiplication and Division
If the signs on the numbers are different, the answer will be negative.
ex. (-3) x (+5) = -15 16 ÷ (-4) = -46 x (-10) = -60
If the signs on the numbers are the same, the answer will be positive.
Fractions Worksheet #1
1. Find an equivalent fraction for each of the following that uses the denominator specified.
a) b) c)
2. Find an equivalent fraction for each of the following that uses the numerator specified.
a) b) c)
3. Reduce each of the following rational numbers to lowest terms.
a) b) c)
d) e) f)
Fractions Worksheet #2
1. Convert each of the following to improper fractions.
a) b) c)
2. Convert each of the following to mixed fractions.
a) b) c)
3. Answer each of the following. Make sure that you express your final answer in lowest terms.
a) b) c)
d) e) f)
g) h) i)
j) k) l)
m) n)
Fractions Worksheet #3
1. Find the lowest common denominator for each of the following fractions.
a) b) c)
2. Answer each of the following. Make sure that you express your final answer in lowest terms.
a) b) c)
d) e) f)
g) h) i)
g) h) i)
Fractions Summary Sheet
Explain each of the following. Use examples in each of your explanations.
1.What is meant by reducing to lowest terms?
2. Explain how to convert between improper and mixed fractions.
3. Explain how to add or subtract fractions.
4. Explain how to multiply and divide fractions.
Conversions
To change a fraction to a decimal you divide the ______by the ______.
To change a decimal to a percent, you multiply by ______.
To change a percent to a decimal, you divide by ______.
To change a decimal to a fraction, you put the entire amount (without the decimal point) over the place value of the last digit.
Since percent means “out of ______”, to change a percent to a fraction, you ______
______
1. Fill in the missing amounts in the following table (Round to 3 decimal places where required)
Fraction / Decimal / Percent50%
75%
0.20
0.40
80%
0.125
0.625
87.5%
30.0%
0.7
4%
2. Write each of the following as a decimal.
a) 19%b) 4%c) 285%d) 0.2%
e) f) g) h)
3. Write each of the following as a percent.
a) b) c) d)
e) 0.57f) 0.6g) 3.14h) 0.004
4. Write each of the following as a fraction (make sure that you reduce to lowest terms).
a) 93%b) 20%c) 5%d) 181%
e) 0.17f) 0.264g) 3.2h) 0.008
5. Find (round to 1 decimal place if applicable):
a) 20% of 20b) 20% of 60c) 15% of 40d) 6% of 150
e) 5% of 35f) 109% of 75g) 4% of 200h) 0.7% of 95
i) 65% of 18j) 112% of 92k) 0.25% of 500l) 115% of 752
Percent Word Problems
1) Mr. Faulds is interested in purchasing a new
bike. The regular price on the bike
is $2499 but it is on sale for 25% off.
a) What is the sale price of the bike?
b) What will the total cost be including the
PST (8%) and GST (7%)?
2) Recently, the Hawaii Ironman was broadcast on television. Of the 2 hours
of coverage, 30% was event history, 20% was commercials and 50% was
actual coverage of the race.
a) How many minutes were spent on commercials?
b) How many minutes were spent on the actual race coverage?
c) How many minutes were spent covering the race history?
3) Peter Reid (a Canadian!!!) has won the Hawaii Ironman World Championships
3 times during the past 8 years. What percentage does this represent?
4) At the Ironman Florida race there were 140 people that dropped out. If
this represented 7% of the people that entered the race, how many were
there at the start of the race?
More Percent Problems
1. Judy earns $16.38 per hour as an accountant. After a good job review, Judy was given a
7.5% pay raise.
a) What is the amount of the raise?
b) What is Judy’s new rate of pay?
2. Allan needs a new bicycle. Doug’s Bicycle has a road bike that normally sells for $1799 on
sale for 20% off the regular price.
a) What is the amount that will be saved if Allan buys the bike?
b) What is the sale price of the bicycle?
3. The Murphy’s have upgraded the insulation in their house and it is estimated that this will
save them 18% on their heating costs this year. If they spent $1046 to heat the home last
year:
a) How much will they save this year?
b) What will the new heating cost be?
4. Dave bought a new snowboard for $499.95. The sales tax (GST & PST) in Ontario is 14%
total.
a) How much tax did Dave pay on the purchase?
b) What was the total amount that Dave paid for the snowboard?
5. Last semester, 60% of the 50 students in grade 9 math earned an A.
a) How many students earned an A?
b) What are two methods that can be used to determine how many students did not earn an
A?
6. Last June, it rained on 22% of the days. How many days did it rain?
7. 15% of a popular radio broadcast is for commercials. In a 1 hour broadcast:
a) How many minutes were spent on commercials?
b) How many minutes were spent on the actual content of the show?
More Percent Problems – Finding the Total
1. On a recent trip, 10% of the passengers became sick. If there were 48 passengers that
became sick, how many were there in total?
2. In a toothpaste test, 30% of the people tested had no cavities. If there were 135 people
with no cavities, how many were tested in total?
3. A soccer stadium was filled to 75% of its capacity. If there were 18 375 people at the
game, what is the capacity of the stadium?
4. You can save $260 on a new home gym if you buy it on sale for 25% off. What is the regular
price of the home gym?
5. At a restaurant, the amount of tip left is usually 15% of the bill when the service is good.
If a tip of $4.25 was left (assuming good service!), what was the amount of the bill?
More Percent Problems – Finding the Rate
1. In one season, a goaltender stopped 395 of the 420 shots that she faced. What percentage
of the shots resulted in goals? (make sure to read this carefully!)
2. 22 out of 30 people surveyed said that they wash their cars on Saturday. What percentage
does this represent?
3. Jamie earned $45 last week and spent $12. Alexis earned $70 and spent $22. Who spent
the greatest percentage of their earnings?
4. Every year, approximately 110 000 people arrive at the Winnipeg airport. If 8550 of them
arrive from Chicago, what is the percentage of travellers that arrive from Chicago?
5. In a course, your term work is worth 70% of your total mark and your final exam is worth
30% of your final mark. If you have a 74% average during the term and get an 80% on the
final exam, what will your final mark be?
Numeracy Extra Practice Questions
Part 1: Estimate the answer to each of the following (do not use your calculator!!!!)
a) 17.9 x 9.5b) c)
Part 2: Answer each of the following integer questions without using your calculator.
a) b) c)
d) e) f)
g) h) i) 4 – (-2) – (-1) + (-7)
j) k) l)
Part 3: Answer each of the following rationals questions without using your calculator.
i) Reduce each of the following to lowest terms
a) b) c) d)
ii) Convert each of the following mixed fractions to improper fractions.
a) b) c) d)
iii) Convert each of the following improper fractions to mixed fractions.
a) b) c) d)
iv) Answer each of the following (Make sure all answers are reduced to lowest terms).
a) b) c) d)
e) f) g) h)
Part 4: Answer each of the following.
i) Convert each of the following to a percent.
a) 0.46b) c) d) 1.37
ii) Convert each of the following to a decimal.
a) 34%b) 0.3%c) d)
iii) Convert each of the following to a fraction.
a) 78%b) 0.435c) 23%d) 1.89
iv) Find:
a) 34% of 200b) 26% of 50c) 115% of 90d) 33.4% of 2000
v) Problems
a) In a recent survey of 250 students, 12% said that their favourite type of movie was
comedies. How many of those surveyed like comedies the most?
b) A DVD player that normally sells for $229 is on sale for 30% off.
i) What is the sale price?
ii) What is the total cost including sales tax (PST = 8% and GST = 7%)?
c) Jessica got a mark of 34 out of 40 on her most recent math test. Samuel is in a
different class and his test was out of 45. His mark was 38. Which student had the
highest percentage on their most recent test?
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