Download Fractions, Decimals and Percents To convert a fraction to a percent

Fractions, Decimals and Percents
To convert a fraction to a percent, convert the fraction to a decimal
number by dividing the numerator by the denominator. Then, multiply
the decimal by 100 and add a percent symbol.
4
= 0.444 44…
9
= 0.444 44… × 100%
= 44.4%
1. Write each fraction as a decimal and a percent.
a) 3 b) 1
4
6
2. Complete the following table.
Fraction
Decimal
Percent
a) 4
5
0.66666….
b)
c) 4
11
d)
33.3%
Probability
The probability of an event is a measure of the likelihood that it will occur.
The probability of an impossible event is 0 or 0%. The probability of a
certain event is 1 or 100%.
A coin is flipped. What is the probability that it lands heads up, P(H)?
Write your answer as a fraction, a decimal, and a percent.
favourable outcomes
P(H) =
possible outcomes
= 1
2
The probability of heads is 1 , 0.5, or 50%.
2
Copyright © McGraw-Hill Ryerson, 2008
.…BLM 11–2.…
(continued)
3. The spinner is spun once. Find the following
probabilities. Write each answer as a fraction,
a decimal, and a percent.
a) What is the probability of spinning 2, P(2)?
b) What is P(< 3)?
c) What is P(> 3)? Justify your response.
Using Tables and Tree Diagrams
Tables and tree diagrams are common ways to organize outcomes.
A coin is flipped and a spinner is spun.
a) What is the sample space or list of
all possible outcomes?
b) How many outcomes are there?
c) What is P(T, 3)?
a)
Table
Coin
Heads (H)
Tails (T)
Tree Diagram
Spinner
1
2
3
H, 1 H, 2
H, 3
T, 1 T, 2
T, 3
b) There are 6 favourable outcomes: (H, 1), (H, 2), (H, 3), (T, 1), (T, 2),
(T, 3).
c) P(T, 3) = 1
6
1
P(T, 3) is , 0.16 , or 16.6% .
6
4. a) Create a table to show the sample space
for the spinner and the fair six–sided die.
b) List the sample space.
c) What is P(A, < 5)?
Copyright © McGraw-Hill Ryerson, 2008
.…BLM 11–2.…
(continued)
5. The following sample space
represents all of the outcomes from
flipping a coin and spinning a
numbered spinner: (H, 1), (T, 1),
(H, 2), (T, 2), (H, 3), (T, 3), (H, 4),
(T, 4).
a) Draw the spinner.
b) Display the sample space in a
tree diagram.
c) What is P(H or T, < 5)? Explain
your thinking.
Multiplying Fractions
You can use paper folding to multiply proper fractions.
To multiply fractions without a diagram, multiply the numerators and
multiply the denominators.
1 1 1×1
× =
2 3 2×3
1
=
6
6. What multiplication statement does
each diagram represent?
a)
7. Multiply. Show your answer in
lowest terms.
a) 3 × 1 b) 3 × 5 c) 4 × 2
4
5
b)
Copyright © McGraw-Hill Ryerson, 2008
5
6
5
3
Name: ________________________________
Date: ________________________
Section 11.1 Extra Practice
.…BLM 11–5.…
Write the answers for #1 to #4 in your notebook.
1. At Antonio’s Pizzeria, the pizzas come in three sizes: large, massive, and
gargantuan. There are four varieties to choose from: Veggie Garden,
Carnivore’s Delight, Cheesy Wheezy, and Hawaiian Paradise. Use either a tree
diagram or a table to display all of the possible choices.
2. Two dice are rolled. One die has the first six prime numbers on it. The other
die has the first six letters of the alphabet on it.
a) What are the possible rolls for each die?
b) Draw a table to show the sample space.
c) What is the total number of outcomes?
d) What is the probability of P(E, 11)? Give your answer as a fraction,
a decimal, and a percent.
e) What is the probability of getting a vowel and an even prime number?
Give your answer as a fraction, a decimal, and a percent.
3. A quarter is tossed into the air and lands. Then, a nickel is tossed into the air.
a) List all the possible outcomes.
b) What is the probability of landing one head and one tail?
c) What is the probability of a head followed by a tail?
d) Explain the difference between P(H, T) and P(H then T).
4. From a deck of cards, use only the hearts to answer the following questions.
Shuffle the hearts and draw from them face down.
a) What is the probability of drawing the six of hearts? Give your answer as a
fraction, a decimal, and a percent.
b) What is the probability of drawing a face card? Give your answer as a
fraction, a decimal, and a percent.
c) What is the probability of drawing the ace of hearts?
d) Suppose you drew a card that was not the ace, kept it out of the pile, and
drew another card. What would be the probability of getting an ace in the
second draw? Give your answer as a percent.
Copyright © McGraw-Hill Ryerson, 2008
Name: ________________________________
Date: ________________________
Section 11.1 Math Link
.…BLM 11–6.…
This worksheet will help you with the Math Link on page 418.
1. Complete the following tree diagram to determine all the possible outcomes
for a toss of four sticks.
2. a) How many possible outcomes are there? ____ How many outcomes have
b) only one decorated side up? ____ c) two decorated sides up? ____
d) three decorated sides up? ____ e) four decorated sides up? ____
f) no decorated sides up? ____
3. What is the probability of exactly three sticks landing decorated side up? Give
your answer as a fraction, a decimal, and a percent.
Copyright © McGraw-Hill Ryerson, 2008
Name: ________________________________
Date: ________________________
Section 11.2 Extra Practice
.…BLM 11–7.…
1. You flip a nickel, a dime, and a quarter.
a) Use a tree diagram to show the number of possible outcomes.
b) Use multiplying to show the number of possible outcomes.
2. Carlos was in charge of purchasing baseball hats for the team.
• He can get them in three colours: blue, green, and black.
• The green and blue hats come in fitted and one-size-fits-all, and in both
washable and non-washable versions.
• Black hats come in only fitted and non-washable styles.
How many hat choices does Carlos have? Show your thinking.
3. At a restaurant, if you order one appetizer, one main course, and one dessert,
you have 72 different meal combinations to choose from. There are three
choices of desserts and four choices of main courses. How many choices of
appetizers are there? Show your thinking.
4. Make up a situation that would give the following number of combinations:
7 × 3 × 2 = 42 combinations.
_______________________________________________________________
_______________________________________________________________
5. Hana won the grand prize trip, but she has some choices to make.
• She can go to Paris, London, or Rome.
• She can go for a week in winter, in spring, or in summer.
• Hana may take her sister or her friend with her, or take nobody and receive
an extra $4500 to spend instead.
How many trip options does Hana have? Show your thinking.
Copyright © McGraw-Hill Ryerson, 2008
Name: ________________________________
Date: ________________________
Section 11.3 Extra Practice
.…BLM 11–10…
Write your answers for #1 in your notebook.
1. Shea-Lee rolled a regular die and recorded the results in a tally chart.
a) How many times in total did
Shea-Lee roll the die?
b) What is the experimental probability
of rolling a 3?
c) What is the theoretical probability of
rolling a 3?
d) Which number’s experimental
probability matches its theoretical
probability?
e) What could Shea-Lee do to get all of
the numbers to match their theoretical probability better?
2. Mallory rolls a six-sided die and Rose flips a coin.
a) Draw a tree diagram in your notebook. What is the probability of the girls
getting tails and an odd number? ____
b) Use multiplication to get your answer. ____________________
c) What is this same probability written as a percent and as a decimal?
____________________
3. Bill and Ravi made two spinners, one with eight equal sectors each with a
different colour, and one with 25 equal sectors each with a different number.
Determine the probability of spinning black and 15 as quickly as possible.
a) Determine P(black, 15). ____________________
b) Write this probability as a fraction, a decimal, and a percent.
____________________
c) Why is calculating the answer easier than drawing a table or a tree
diagram?
_____________________________________________________________
4. Ivan created a spinner for a simulation. He knew the
theoretical probability for an event was 2 . This is the
3
spinner he created. Is this a fair spinner for the simulation?
Explain your thinking.
_______________________________________________________________
Copyright © McGraw-Hill Ryerson, 2008
Chapter 11 BLM Answers
BLM 11–2 Chapter 11 Get Ready
1. a) 3 = 0.75 = 75% b) 1 = 0.16 = 16.6%
4
6
2.
Fraction
Decimal
Percent
0.8
80%
a) 4
5
b) 2
3
0.66666….
66.6%
c) 4
11
0.3636….
36.36%
d) 1
3
0.33333….
BLM 11–5 Section 11.1 Extra Practice
1.
Large
Massive
Gargantuan
Veggie
Garden
Veggie
Garden
Veggie Garden
Carnivore’s
Delight
Carnivore’s
Delight
Carnivore’s
Delight
Cheesy
Wheezy
Cheesy
Wheezy
Cheesy
Wheezy
Hawaiian
Paradise
Hawaiian
Paradise
Hawaiian
Paradise
33.3%
3. a) 1 , 0.3 , 33.3% b) 2 , 0.6 , 66.6%
3
3
0
c) , 0.00, 0%. There are no numbers greater than 3
3
on the spinner so there is 0 probability.
4. a)
1
2
3
4
5
6
A
A, 1
A, 2
A, 3
A, 4
A, 5
A, 6
B
B, 1
B, 2
B, 3
B, 4
B, 5
B, 6
b) (A, 1), (A, 2), (A, 3), (A, 4), (A, 5), (A, 6),
(B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)
c) P(A, < 5) = 4 or 1
12
3
5. a)
b)
c) P(H or T, < 5) = 100%. Every outcome in the
sample space will consist of either a head or a tail
and a spin of less than 5.
6. a) 2 × 1 = 1 b) 3 × 2 = 1
3
2
3
4
3
2
7. a) 3 b) 1 c) 8
20
2
15
Possible number of choices: 12
2. a) Die 1: 2, 3, 5, 7, 11, 13; Die 2: A, B, C, D, E,
F
b)
2
3
5
7
11
A
A, 2
A, 3
A, 5
A, 7
A, 11
A, 13
13
B
B, 2
B, 3
B, 5
B, 7
B, 11
B, 13
C
C, 2
C, 3
C, 5
C, 7
C, 11
C, 13
D
D, 2
D, 3
D, 5
D, 7
D, 11
D, 13
E
E, 2
E, 3
E, 5
E, 7
E, 11
E, 13
F
F, 2
F, 3
F, 5
F, 7
F, 11
F, 13
c) 36 possible outcomes
d) P(E, 11) =
= 0.02778 = 2.778%
1
36
e) P(vowel, even prime number) =
2
36
= 0.05 = 5.556%
3. a) quarter head, nickel head; quarter head,
nickel tail; quarter tail, nickel head; quarter tail,
nickel tail b) P(H, T) =
1
2
c) P(H followed by T) =
1
4
d) Answers will vary. Example: P(H, T) and P(H
then T) are different because the second one is
more specific than the first. P(H, T) means that
either the quarter or the nickel can be heads or tails,
while P(H then T) means that the quarter must be
heads and the nickel must then be tails.
4. a)
, 0.077, 7.69% b)
, 0.231, 23.1%
3
1
13
13
c) 7.78% d) second draw
1 = 8.3%
12
BLM 11–10 Section 11.3 Extra Practice
1. a) 60 b)
=
c)
d) 4
12
1
1
60
5
6
e) Answers will vary. Example: Roll many more
times.
2. a)
BLM 11–6 Section 11.1 Math Link
1.
3
12
b)
2. a) 16 b) 4 c) 6 d) 4 e) 1 f) 1
3. 4 , 0.25, or 25%
16
BLM 11–7 Section 11.2 Extra Practice
1. a)
b) 2 × 2 × 2 = 8
2. four kinds of blue, four kinds of green, two kinds
of black = ten choices
3. 3 × 4 ×
= 72. There are six choices of
appetizers.
4. Answers will vary. Example: 7 days a week × 3
meals a day × 2 types of beverages = 42 beverage
choices each week
5. 27
3
6
×
1
2
=
3
12
or
1
4
c) 25%, 0.25
3. a) 1 × 1 = 1
b) 1 , 0.005, 0.5%
8
25
200
200
c) Answers will vary. Example: A table or tree
diagram would take too long to draw and be very
complicated. Calculation is much quicker.
4. Answers will vary. Example: This is a fair spinner
because 10 of the 15 sections are shaded. The
probability of spinning a shaded section is .
2
3