Final Exam Review

1
Final Exam Review Numbers
2
Numbers Numeration Review

• The Math 8 Final Exam will test, among other
  things, how well you can do algebra, geometry,
  proportions percents, number sense patterns
  and graphing.

3
Algebra

• The algebra questions you see on your final will
  fall (for the most part) under six
  classifications.

Factors Multiples
Integers
Fractions
Numeration
Exponents
Miscellaneous
Percents
4
Numbers

• This section deals with numbers and numeration.
  You will do a question or two on each slide. If
  you get it right, just go on to the next slide.
  If you get it wrong, click the arrow at the
  bottom of the page to complete a tutorial on that
  kind of equation. Be absolutely positive that
  you write your work on scrap paper and you will
  have to hand it in for credit. Click the arrow
  to begin.

Click to Begin
5
Number Sense

• Lets see if you know your integer rules.
• 5 (-7) 7) -2 x 9
• -3 (-1) 8) -2 x -9
• -4 9 9) 5 x -4
• 5 (-2) 10) -10 x (-5)
• 2 5 11) 15 / (-5)
• -7 3 12) -15 / (-5)

-18
-2
18
-4
-20
5
7
50
-3
-3
-10
3
6
Use the order of operations to simplify
expressions. Do you know it?

• Simplify each
• 18 5 3
• 50 - 49
• If a 5 and b 3, evaluate ab2
• If a 4, b -3 and c 5, evaluate
• a(b c) (a b)

16
14
45
1
7
Be able to express large and small numbers in
scientific notation. Do you know it?

• Express each in scientific notation
• 872,000,000
• 0.00000104

8.72 x 108
1.04 x 10-6
8
Be able to identify between what two integers the
square root of an irrational number lies. Do you
know it?
1) Between what two rational numbers does the
square root of 42 lie? A) 4 and 5 B) 6 and 7 C)
8 and 9 D) 40 and 50
b
9
Be able to identify rational and irrational
numbers. Do you know it?
Identify each number as rational or
irrational 1) 2.5 2) ? 3) 5/8 4)
3.1212.. 5) 19.23242537829..
rational
rational
irrational
rational
Irrational if it keeps repeating with no pattern.
10
Evaluate Expressions with Integral Exponents. Do
you know it?

• 34
• 50
• 102
• 4) 17
• 5) 25

81
1
100
1
32
11
Convert fractions, decimals and percents. Do you
know it?

• Express 25 as a decimal.
• Convert 0.03 to a percent.
• Express 3/8 as a percent.
• Convert 3/10 to a percent.

0.25
3
37.5
30
12
Read, write and identify percents. Do you know
it?

• Express 25 as a fraction in simplest form.
• Convert 0.44 to a fraction in simplest form.
• Express 3/4 as a percent.
• Convert 3/25 to a percent.

1/4
11/25
75
12
Any wrong on the last 2 slides.....
13
Be able to find the missing piece of the percent
proportion. Do you know it?
1) What is 35 of 180?
63
2) What of 80 is 20?
25
3) 20 of what number is 15?
75
14
Be able to find the missing piece of the percent
proportion. Do you know it?
1) 25 of the fish Rob catches are striped bass.
If he catches 32 fish, how many are striped bass?

8
2) Jenny did a great job on her math test when
she got 19 out of 20 questions correct. What
percent did she get right?
96
3) Dave Kingman is a former pro ball player who
used to hit a lot of home runs. One year, 34 of
his hits were home runs. If he had 51 home runs,
how many hits did he have?
150
If you missed any on the last two slides, click...
15
Find the Greatest Common Factor (GCF) and Least
Common Multiple (LCM.) Do you know it?
1) Find the greatest common factor of 15 and
20. 2) Find the greatest common factor of 12
and 24. 3) Find the least common multiple of 15
and 20. 4) Find the least common multiple of 6
and 8
5
12
60
24
16
Apply the GCF and LCM. Do you know it?
1) Mr. Fren is stopped at a traffic light. The
two cars in front of him are both turning. One
cars blinker flashes every 4 seconds and the
other every 5 seconds. At how many seconds will
the blinkers flash simultaneously? 2) Mr. Bruno
has one class with 18 students and another class
with 24 students. If Mr. Bruno wants to sit the
students in the biggest groups possible so that
everyone has a seat and there are no students
leftover, how big should the throats.
20
6
17
Find the prime factorization of a number. Do you
know it?
Find the prime factorization of 60. Find the
prime factorization of 100.
22x3x5
2 x 2 x 5 x 5 or 22 x 52
18
Conversions

• Convert each of the following
• 1) 2 Tons _______ pounds
• 2) 60 inches _______ feet
• 3) 5,000 km _______ meters

4,000
5
5
19
Convert Units of Capacity and Volume.
Conversions provided on formula sheet 1 cm 10
mm 1 cup 8 fluid oz 1 m 100 cm 1000 mm 1
pint 2 cups 1 km 1000 m 1 qt 2 pints 1
gram 1000 mg 1 liter 1000 ml 1 kg 1000
g 1 kl 1000 liters 1 pound 16 oz 1 ton
2000 lbs
1) Lisa bought 2 gallons of soda. What is the
measure in pints? A) 4 B) 8 C) 16 D) 32
20
Conversions provided on formula sheet 1 cm 10
mm 1 cup 8 fluid oz 1 m 100 cm 1000 mm 1
pint 2 cups 1 km 1000 m 1 qt 2 pints 1
gram 1000 mg 1 liter 1000 ml 1 kg 1000
g 1 kl 1000 liters 1 pound 16 oz 1 ton
2000 lbs
1) Emilia drank 2,000 milliliters of milk
yesterday. What is the measure in liters? A) 2
L B) 20 L C) 200 L D) 2,000 L
21
Conversions provided on formula sheet 1 cm 10
mm 1 cup 8 fluid oz 1 m 100 cm 1000 mm 1
pint 2 cups 1 km 1000 m 1 qt 2 pints 1
gram 1000 mg 1 liter 1000 ml 1 kg 1000
g 1 kl 1000 liters 1 pound 16 oz 1 ton
2000 lbs
Candice is making a pitcher of lemonade. She
used 6 pints of water. How many cups is this?
12 cups
22
Convert Units of Mass.
Conversions provided on formula sheet 1 cm 10
mm 1 cup 8 fluid oz 1 m 100 cm 1000 mm 1
pint 2 cups 1 km 1000 m 1 qt 2 pints 1
gram 1000 mg 1 liter 1000 ml 1 kg 1000
g 1 kl 1000 liters 1 pound 16 oz 1 ton
2000 lbs
Tonys car weighs 3,400 pounds. How many tons is
this? A) 1 ton B) 1.5 tons C) 1.7 tons
D) 2 tons
Click here when done converting
23
Integers!!!
Absolutely, positively everything you need to
know!
24
Adding Integers

• There is one question you need to ask yourself
  when adding integers Are the signs the same?

Are the signs the same?
No
Yes
Subtract. Keep Sign of bigger .
Add. Keep sign.
25
Adding Integers Same Sign

• Remember Add and keep the same sign!
• 3 (5)
• -3 (-5)
• 7 4
• -7 -4
• -3 (-100)
• -2 -2
• -12 (-3)

8
-8
11
-11
-103
-4
-15
26
Adding Integers Different Signs

• If the signs are different, subtract and keep the
  sign of the bigger number.
• 5 (-3)
• 5 (-4)
• 5 -5
• 5 (-6)
• -3 4
• -9 7
• 8 -5

2
1
0
-1
1
-2
3
27
How Many Can You Get?
2
-5

• -3 5 6) -2 -3
• 7 8 7) 9 -9
• 1 -5 8) -7 (-7)
• -10 -5 9) -4 1 8
• -8 -2 10) -2 (-1) (-4)

15
0
-4
-14
-15
5
-10
-7
You understand when you can get 9 or more right ?
!
28
Subtracting Integers

• If you let it, subtracting integers can get very
  confusing. If you are having trouble, lets try
  a new way and hope we dont get confused. DONT
  SUBTRACT!!!! Thats right lets add instead
  after all, you already know how to add!
• The hardest part of integers is when all of the
  different rules start confusing us. We already
  know the rules for adding, so lets just add.
  The only thing we have to remember is that the
  sign in front tells us whether the number we are
  adding is positive or negative.
• Heres what I mean 4 2 can also mean (4)
  plus (-2). So just read it that way. 4 (-2)
  2. Lets try another
• 5 7 should be read as 5 -7. And we
  already know that is 2.

29
Practice. Practice. Practice.

• Question Conversion Answer
• 3 7
• -5 2
• -8 2
• -4 4
• 9 - 5

-4
3 plus -7
-7
-5 plus -2
-10
-8 plus -2
-8
-4 plus -4
4
9 plus -5 OR just 9 - 5
30
The Last Detail of Subtraction

• In case you had not noticed, the last set of
  problems lacked the type of question that looked
  like 5 (-3). Lets just write this as 5 -
  (-3). In order to do this type, we need to
  remember that when you negate or minus ( - ) a
  negative, you make a positive. So 5 (-3) is 5
  3.
• Question Conversion Answer
• 4 (-5) 4 5 9
• 2 (-3)
• -5 (-2)
• -4 - 10

2 3
5
-3
-5 2
-4 plus -10
-14
31
Subtraction Practice

• Question Conversion Answer
• 7 (-3)
• 5 8
• - 7 2
• 10 (-5)
• 3 - 7

10
7 3
-3
5 plus -8
-7 plus - 2
-9
10 5
15
-4
3 plus - 7
32
What Do We Know So Far?
add

• When you add and the signs are the same, you
  ______ and keep the ____________.
• When you add and the signs are different, you
  _________ and keep the _____________________.
• DONT Subtract!!!! Treat the problem like
  _________ and the sign in front tells you if it
  is ___________ or ___________. If you see two
  negatives in a row (like 5 (-2) ), change the
  - - to a ___.

same sign
subtract
sign of the bigger number
addition
positive
negative

33
Addition/Subtraction Mixed Bag

• 8 -4 6) -3 9
• 12 (-5) 7) -10 (-2)
• -2 1 8) 5 -4
• -3 -4 9) 7 (-7)
• -4 -1 -3 10) -4 (-1) -7

4
-12
17
-8
-3
1
-7
0
-8
-10
34
Multiplication Division

• There are several ways to explain multiplying and
  dividing with signed numbers, but lets try a
  less common method. Heres the deal just
  multiply (or divide) the numbers and only when
  you are doing so BY a negative do you change the
  sign. Its easy!
• Question Thought Process Answer
• -3 x 5 3 times 5 is 15 and keep the neg. -15
• -3 x -5 -3 x 5 is -15, BUT -5 means change sign
  15
• 8 x -4 8 x 4 32,BUT -4 means change sign -32
• -5 x -9 -5 x 9 45, BUT -9 means change sign -45

35
Multiplication and Division Practice
10
-5

• -5 x 2 5) (-10) / 2
• -18 / 9 6) -1 x -3
• 12 / -4 7) -10 x -8
• 5 x -5 8) -20 / 5

-2
3
-3
80
-4
-25
In s 1, 3, 4, 6 and 7, you multiplied or divided
BY a negative, so the sign changed. In all of
the others, you multiplied or divided BY a
positive, so it stayed the same ? !
36
Completely Mixed Practice
2
24

• 7 (-5) 6) -3 x -8
• -3 (-4) 7) 8 10
• -22 / 11 8) -9 (-2)
• -6 x -5 9) 10 (-4)
• -4 3 10) -25 / -5

-2
1
-2
-11
14
30
-1
5
37
Order of Operations
Absolutely, positively everything you need to
know!
38
The Order of Operations

• The order or operations tells us what to do and
  when to do it when trying to evaluate an
  expression. Some people remember PEMDAS and
  others PLEASE EXCUSE MY DEAR AUNT SALLY. Either
  way, it all means the order is
• Parenthesis (aka Packages)
• Exponents
• Multiplication / Division (left to right, they
  are equal)
• Add / Subtract (left to right, they are equal)

39
What Operation Do You Do First?

• 9 2 9
• 17 4 x 5
• 10 (5 3)
• 10 14 2
• 83 5 x 100

subtract
multiply
subtract
divide
exponent
40
Step by Step Order of Operations

• Go slow and answer this question step by step.
  As you click on the mouse, each step will appear.
• Evaluate 25 3 x 22

OK. First you have to do 22 4
So it becomes 25 3 x 4
Next you have to do 3 x 4 12
Finally, it is 25 - 12
13
41
Lets Do Another Step BY Step

• Evaluate 5(7 3) 8 1

First things first do the package 7 3 4
So we have 5(4) 8 1
I sure hope you realize multiplication comes
next. 5 x 4 20
OK. Now 20 8 1
Dont get fooled!!! Addition and subtraction are
equal. 20 8 12
Finally, 12 1
13
42
Perfect Practice Makes Perfect

• 5(7 9) 3) 2(4 3)2
• 2) 22 7 10 2 4) 102 43

2(7)2 2 49 98
5 (-2) -10
22 7 5 15 5 20
100 64 36
43
Algebra The Order of Operations

• Use the values a 10, b -5, c 4, d 2 and e
  -2
• 1) ab2 2) e3 ab 3) ac be

(-2)3 10(-5) -8 10(-5) -8 (-50) -58
10 4 (-5)(-2) 40 10 50
10 (-5)2 10 25 250
44
Summary

• The Order of Operations is
• Parenthesis (aka Packages)
• Exponents
• Multiplication / Division
• Addition / Subtraction
• DANGER!!! Be very careful with the last two
  steps. Multiplication and Division are equal to
  each other. If they are the only steps
  remaining, just go left to right.
• The same holds true for addition and
  subtraction.

45
Scientific Notation

• Scientific notation is most commonly used as a
  shortcut for expressing and working with large
  and small numbers. In general, the format for a
  number expressed in scientific notation is
• What is wrong with each of these?
• 235,000 235 x 103
• 5,000,000 5 x 56

(Number between 1 10) X 10 places decimal moves
Numbers is not between 1 10
The base is not 10, it is 5
46
Express in Scientific Notation

• 42,000,000,000
• 705,000

4.2 x 1010 Some common mistakes are . 42 x
109 (42 is not between 1 10) .42 x 109 (.42 is
not between 1 10)
7.05 x 105 Some common mistakes are .. 705 x
103 (stopped moving the decimal as 0s
stopped) 70.5 x 104 (70.5 is not between 1 10)
47
Scientific Notation Done Right

• Convert 52,000,000,000 to scientific
  notation.
• Convert 0.00000073 to scientific notation.

10 places to move
We need to get the number into proper form. So
. In order to get 52,000,000,000 to proper form
I need to move the decimal (and count) until I
get 5.2. The answer is 5.2 x 1010
7 places to move
Now we need to move the decimal to the right
until we get a number between 1 10. Count the
places! The exponent is negative because the
number is small (0.0000) The answer is 7.3 x
10-7
48
Perfect Practice Makes Perfect

• 507,000 3) 11,000,000
• 0.0000004 4) 0.00000003108
• 5) The sun is 93,000,000 miles from the earth.
  Express this number in scientific notation.

5.07 x 105
1.1 x 107
4 x 10-7
3.108 x 10-8
9.3 x 107
49
Rational Irrational Numbers

• Rational and irrational numbers are the two basic
  types of real numbers. Each has can be defined
  in terms of fractions and decimals.

50
Irrational Numbers

• The two most famous irrational numbers are p and
  a square root that is not perfect, like .
  If a square root is perfect, like , it is
  rational.
• Label each as rational or irrational. If
  rational, compute the root
• 
  

irrational
irrational
rational, 10
51
Classifying Numbers Rational or Irrational

• Classify each of the numbers below as rational or
  irrational. Give a reason why.
• 1) 29/4 2) 7 3) 2.181818 ..

These numbers are all rational. The first and
second are fractions, so they are obviously
rational by definition. The third is rational
because it is a decimal that repeats. The two
main irrational numbers are p and any square root
you can not figure out.. Like the square root of
5. The square root of 9 is rational because it
is 3.
52
Evaluating Integral Exponents

• An exponent means how many times you use the base
  as a factor. So, for instance, 53 means 5 x 5 x
  5 and this is equal to 125. The most common
  mistake kids make is to confuse an exponent with
  multiplying. 53 is NOT 15!
• Fill in the missing part below
• Exponent Form Factors Form Value
• 72
• 10 x 10 x 10
• 34
• 2 x 2 x 2 x 2 x 2

7 x 7
49
1,000
103
81
3 x 3 x 3 x 3
25
32
53
Other Exponents

• There are two other exponent situations you need
  to be prepared for.. When the exponent is 0
  and when, for a base of 10, the exponent is
  negative.
• Case 1) Anything to the zero power 1!
• Case 2) The base 10 to a negative power
  0.something.
• 1) 50 2) 70 3) 90
• 4) 10-1 5) 10-2 6) 10 -3

1
1
1
0.1
0.01
0.001
54
The Perpetually Problematic Percents

• Percents drive some kids NUTS! One big reason
  for that is that you dont solve all of the
  problems the same way. First the bad news Any
  student who just wants to be told what to do
  instead of having to think with percents is going
  to have a hard time. Now the good news Any
  student willing to remember and work with a
  couple of basic ideas can master percents. Key
  ideas
• Percent means out of 100.
• The percent is the part out of 100.
• Fractions, decimals and percents are all the same
  thing (like hello, hola and bon jour).

55
Percent Means out of 100

• Simply put, percent means out of 100. So if 55
  out of 100 dentists prefer Trident gum, 55
  prefer it.
• If 99 out of 100 students think Math is the best
  subject, 99 think Math is the best subject.
• But what percent think Math is the best subject
  if only 2 out of 5 think it is the best? Do you
  know what a lot of students write? 2!!!!! Can
  you believe that? The question said 2 out of 5
  not 2 out of 100! To find the percent we must
  find out how many out of 100.

56
Converting Between Decimals and Percents

• Converting between decimals and percents is one
  of he easiest math skills. Remember, percent
  means out of a hundred. Also remember that two
  decimal places is the equivalent of 100.
• to Decimal Decimal to
• Move decimal 2 places left 2 places right

Percents are bigger so we move to the right
Examples 50 .50 (or just .5) .721
72.1 11 .11 (2 places only) .005 0.5 (2
places)
57
Converting to a Percent

• There are two main ways to convert fractions like
  2 out of 5 (2/5) to a percent.

2/5 means 2 5 which is .4000. To convert to
a percent, move the decimal two places right or
40.
since 5x20 100, 2x2040 40/100 40

• 2 ?
• 5 100

Convert each to a percent 1) 7/10 2) 3 out of
25 3) 3/8
70
12
37.5
58
Convert Percent to a Fraction

• To convert a percent to a fraction, just write it
  out of 100 and reduce if necessary.
• 25 25 out of 100 25/100 reduced ¼. Now
  you try.

45
45 out of 100 45/100 reduce to 9/20
90
90 out of 100 90/100 reduce to 9/10
37
37 out of 100 37/100 this is reduced.
What if we get one like 37.5? Then we need to
do 37.5/100 but this looks funky. Convert to
375/1000 to get rid of the decimal (move
numerator denominator one place each. You try
31.7.
31.7 out of 100 317/1000
59
Perfect Practice Makes Perfect

• Convert each to a percent
• 1) 0.57 2) 12/100 3) 12/50
• 4) .393 5) 5/8 6) 0.001

12
24
57
393
62.5
0.1

• Convert each to a decimal
• 77 8) 29 9) 0.2
• 10) 45 11) 100 12) 25.5

0.77
0.29
0.002
1
0.255
0.45
60
Converting to Fractions

• We already discussed how, in order to go from a
  percent to a fraction, we should put it over
  or out of 100 and reduce. To go from a decimal
  to a fraction is just as easy. Just read it
  properly and reduce . Remember, one decimal
  place is tenths, two are hundredths, three
  thousandths and so on. For example
• 0.5 read properly is 5 tenths 5/10 ½.
• 0.34 read properly is 34 hundredths 34/100
  17/50
• 1.233 read properly is 1 and 233 thousandths
• 1 233/1000

61
Perfect Practice Makes Perfect

• Convert to a fraction in simplest form
• 1) 0.1 2) 0.79 3) 0.433
• 0.38 5) 75 6) 0.009
• 7) 97 8) 0.747 9) 0.5

1/10
79/100
433/1000
19/50
3/4
9/1000
97/100
747/1000
1/200
62
Fractions, Decimals, Percents Summary

• Besides remembering that fractions, decimals and
  percents are just different ways of saying the
  same thing, we need to remember how to convert
  amongst them.
• Decimals and percents move the decimal ________
  places to the ________ for a percent and
  _________ for a decimal.
• Decimals to fractions you just ______ properly
  and _______. Fractions to decimals you just
  ________.
• Percents to fractions, just put it ______ 100.

two
right
left
read it
reduce
divide
over
63
The Percent Proportion

• Most students use the percent proportion in
  percent problems, so we will might as well, too.
  The percent proportion is
• Your job as a student is to determine what number
  goes in which place. Now, the 100 always stays
  where it is. The word is usually tells the part
  and of usually tells the whole. A lot of people
  think underlining can be a big help in these word
  problems. DONT try to solve the question right
  away try to find the parts.

Percent part (is) 100 Whole (of)
64
Solving in the Percent Proportion

• Find the missing part of each equation. Remember
  identify the percent, the part (is) and the
  whole (of.) Finish by substituting the correct
  values.
• 1) What is 18 of 50? 2) 20 is what percent of
  25?

part (is) 100 whole (of) n
20 100 25 25n 2000 n 80
part (is) 100 whole (of) 18
n 100 50 100n 900 n 9
65
Problem One

• Jenny takes a science test that has 25 questions.
  She gets 21 of them right. What percent did
  Jenny get right?

First things first . Lets underline the
important stuff!
Two numbers are underlined, 21 and 25. Which one
represents the whole number of questions and
which one the part?
part Now the part 21 and whole
25, so 100 whole
N 21 cross multiply 25n 2100 100
25 25
25 n 84
66
Problem Two

• Remember, find the important stuff and
  underline!!!!!
• In order to pay her way through college, Tammy
  works and earns 800 a month. If 65 of this
  money goes to tuition, how much money does Tammy
  spend each month on tuition?

The whole amount Tammy earns is 800
part (is) 100 whole (of)
65 n 100 800
100 n 52,000 n 520
67
Factors and Multiples

• For some reason, factors and multiples often give
  students a difficult time. Lets try to relate
  each concept to its name.
• Multiples are linked to multiplying and
  (ordinarily) multiplying makes things bigger. So
  multiples are bigger!
• Factors are smaller. One way to remember this is
  that many small factors go into a big decision
  . or remember that factoring is division so
  factors divide into and are going to be smaller.

68
List the Factors and Multiples

• 1) What are the factors of 12?
• 2) What are the multiples of 12?
• 3) What are the factors of 20?
• 4) What are the multiples of 20?
• 5) What are the multiples of 15?
• 6) What are the factors of 15?

1, 2, 3, 4, 6, 12
12, 24, 36, 48, 60,
1, 2, 4, 5, 10, 20
20, 40, 60, 80, 100,
15, 30, 45, 60, 75, 90,
1, 3, 5, 15
Factors stop. Multiples keep going and going
69
GCF LCM

• The Greatest Common Factor is the biggest number
  that divides into both numbers. Find the GCF of
• 1) 15 20 2) 40 60 3) 12 30
• The Least Common Multiple is the smallest
  multiple of both numbers. Find the LCM of
• 4) 15 20 5) 6 8 6) 9 12

6
5
20
24
36
5
70
Prime Factorization

• Prime factorization is factor trees. Find the
  prime factorization of .
• 20 120

10
12
10
2
2
5
4
3
5
2
2
2
The answer is 2 x 2 x 5 or 225
23x3x5
71
A box of Corn Flakes cereal sells for 3.78. The
volume of the box is 18 ounces. What is the unit
price for an ounce of Corn Flakes?
unit means one so the question is saying what
is the price for one ounce. 3.78 18 ounces
0.21 per ounce
72
More Practice

• John Haag was a locally famous fly tier on Long
  Island. He used to buy enormous quantities of
  feathers. He would buy 5 pounds of feathers for
  240.00. What was the unit price (per ounce)
  that John paid for feathers?

dollars dollars ounces ounces
80 n 240 n 3
(16 oz)(5lbs) 80
240 n 80 oz 1 oz
73
Costco sells two different size packages of
chicken. One package sells 3.5 pounds for 8.19
and the other sells 5 pounds for 10.79. Which
one is a better buy and how much do you save per
pound?
8.19 3.5 2.34 10.79 5 2.158
2.16 2.34 - 2.16 0.34 The 5 lb bag is
cheaper by 0.18 per pound.
74
Emily babysits in order to make some money. On
Saturday, she gets paid 12 for 2.5 hours of
babysitting. On Monday, she gets paid 30. How
long did Emily babysit?
dollars dollars hours hours
12n 75 n 6.25
12 30 2.5 n
Emily works 6.25 hrs.
75
Perfect Proportion Practice

• Mr. Lindquist goes fishing for rainbow trout. In
  his first 2.5 hours of fishing, he catches 10
  beautiful rainbow trout. At this pace, how long
  will it take Mr. Lindquist to catch 18 trout?

time time trout trout
10 n 45 n 4.5
2.5 n 10 18
It takes Mr. Lindquist 4.5 hours
76
Perfect Practice Makes Perfect

• One dozen tomatoes cost 3.15. How much do 30
  tomatoes cost?

dollars dollars tomatoes tomatoes
3.15 n 12 tom. 30 tom.
12 n 94.50 n 7.875 n 7.88
77
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