Felipe Sanchez
Rachel Coombs
Isabel Botero
Tomas Iezen
Rachel Coombs
A
proportion is an equation stating
that 2 ratios are equal.
A ratio is the comparison of 2
numbers.
4/16 = X/2
4/16 = X/2
First, you must get X by itself. The opposite of division
is multiplication, so you divide by 2 on each side.
2● 4/16 = 2● X/2
That cancels out 2, so all you have left to do is
multiply 2 by 4/16.
2● 4/16 = .5
X = .5
Tim wanted to know the colors of hair
of people compared to others.
Hair colors
Grade
Brown Hair
Black Hair
Blonde Hair
Red Hair
7th Grade
12
4
10
1
8th Grade
12
6
9
0
7th graders with brown hair to 8th graders with
brown hair: 12:12
Red heads to students in 7th grade: 1:27
Black haired 8th graders to blonde haired 7th
graders: 6:10
Rachel Coombs
Biologists
need to know the
population number of types of
animals in a habitat. Instead of
counting each animal, they have a
process called capture-recapture.
Biologists have tagged 120 fish in a lake.
The results say they have only tagged 13%
of the fish. You need to figure out how
many fish there are in the lake.
First, you need to write a proportion. Since percents are always out of 100, you
can write 13/100. Then you have the number of tagged fish, (120) over the
unknown total of the population. (X)
13/100 = 120/X
You have to invert both the ratios, which is done just by flipping the numbers.
100/13 = X/120
Then you just solve the proportion! The opposite of division is multiplication,
so you multiply by120 on both sides, which cancels out 120.
120●100/13 = X
923 = X
There are 923 fish total in the lake.
Biologists have tagged 80 fish in a
lake, they put them back in. when
they take them back out, 14 percent
of them are tagged.
First, you need to write a cross-product
property. You do 14/10: 80/x
80 ● 10 = 800
800 / 14=57.142
There is an estimate of 57 fish in the lake
You have tagged 214 fish in the lake.
The results say there is a total of 1051
fish in the lake. You need to find the
percent of fish you’ve tagged.
The percent will be out of 100, so you have the percent, (X) over
100. Then you have the amount of tagged fish, (214) over the
total of fish in the lake, (1051).
X/100 = 214/1051
The opposite of division is multiplication, so you must multiply
by 100 on each side to undo the division. That cancels out the
100.
100●214/1051 = X
20 = X
You have captured 20% of the fish in the lake.
Felipe Sanchez
 These
are the processes used to convert
data into other units or to find data
values by converting another unit. This
is used to compare money and
measurements among others, for
instance converting centimeters into
inches. The process of the conversion
goes by a the cross-product-property
rule, also known as the rule of 3.
Proportions are set up by ratios.
Students in Mr. Osborn’s class measured several
objects in centimeters and want to convert the
measurements to inches. They are using the ratio
from inches to centimeters: 1:2.4
Mr. Osborn’s Class Measurements
Object #
Centimeters
Inches
1
4.8
2
2
10
4.16
3
2
0.83
4
50
20.83
5
32
13.33
6
95
39.583
7
69
28.75
8
16
6.66
9
5.4
2.25
10
47
19.583
Food Sendings
Paul is sending a car with the food bought by chef Collins,
he measured the weight of the total amount of each item in
grams, but chef Collins wanted the measurements in ounces.
Paul must change the measurements. He’ll use the ratio from
grams to ounces of 28.4:1
Food Type
Weight in Grams
Weight in Ounces
Steak
500
17.605
Potatoes
600
21.126
Tomato
300
10.563
Lettuce
200
7.042
Eggs
800
28.169
Chicken
1100
38.732
Spices
100
3.521
Apples
150
5.281
Corn
1000
35.211
Felipe Sanchez
A
direct variation is a situation in a set of
data in which both columns of values (or
x and y) grow or decrease at the same
rate. As one grows the other one grows
and vice-versa . But for it to officially be
a direct variation both must grow or
decrease at a constant rate.
The Smiths are going on a road trip to
the Grand Canyon and they’re going
at a constant speed of 100km/hour.
Road trip Distances
Hours traveled
Kms traveled
1
100
2
200
3
300
4
400
5
500
6
600
7
700
8
800
9
900
10
1000
Toby has been having trouble with math and science so he set
up a studying schedule. He studied for one hour and divided it
into 3, two thirds (40 minutes) for math and one third (20
minutes) for science. Sadly he failed the tests so every week he
added more time to his studying.
Total time studying
Time studying math
Time studying science
1 hour
40 minutes
20 minutes
1.5 hours
60 minutes
30 minutes
2 hours
80 minutes
40 minutes
2.5 hours
100 minutes
50 minutes
3 hours
120 minutes
60 minutes
3.5 hours
140 minutes
70 minutes
4 hours
160 minutes
80 minutes
4.5 hours
180minutes
90 minutes
5 hours
200 minutes
100 minutes
Isabel Botero
A relationship in which the product
of two variables is constant.
A relationship in which two variables
are inversely proportional
Equation

Sofia measured the force needed to open a door by pushing
at different distances form the hinge.
Distance (cm)
from hinge
Force (N)
40 cm
20.9
45 cm
18
50 cm
16.1
55 cm
14.8
60 cm
13.3
65 cm
12.3
You can see that as the distance
increases, force decreases.
Camila measured amount of time taken to walk a
kilometer in different speeds
Speed (meters
per min.)
Time (min.)
As the speed increases the time
decreases.
1 meters
1000 min.
2 meters
500 min.
T=k/m
3 meters
333.333 min.
4 meters
250 min.
5 meters
200 min.
6 meters
166.666 min.
T=time
K=kilometers
M=mt/min
Isabel Botero
Order of operations is done in order to
avoid confusion. It is a set of rules that
are followed so that a written
mathematical expression is read and
evaluated the same by everyone.
 You can use PEDMAS do remember the
order. Parenthesis Exponents Division
Multiplication Addition Subtraction

Bob invented a math magic trick. Which always gives him
the same answer and uses order of operations. He tried it on
Laura and Camilo
Directions
Laura’s sequence
Camilo’s sequence
Pick a number from 1-15
7
10
Add 9 to it
16
19
Multiply the result by 3
48
57
Subtract 6 to your answer
42
51
Divide this answer by 3
14
17
Subtract your original
number
7
7
Equation: 3(x+9)-6
----------- -x
3
Veronica has a math test and she has to do order of
operations right. Here is the equation she is given. It is a
math trick and she has to figure out what is the order
1. Pick a number
2. Add 7
3. Divide the answer by 4
4. Add 5
5. Multiply the answer by 4
6. Subtract your original number
7. Add 13
Isabel Botero

Undoing operations is a method of
solving an equation by working
backwards to reverse each
operation until the variable is
isolated on one side of the equation.
Laura has organized what she is going to do to undo an
operation in a graph.
Operation
Undoing operation
Result
x
--------------------------------- 18
X+3
-3
21
2(X+3)
/2
42
2(x+3)
--------6
×6
7
A math problem gives Carlos y=28 as a result but he doesn’t
know what the x is. He uses order of operations
Description
Sequence
Expression
Undo
Result
Pick a number ?
X
------------------
84
Divide by 6
Ans/6
X/6
●6
14
Add 4
Ans+4
x/6 + 4
-4
18
Multiply by 2
Ans●2
2 (x/6 +4)
/2
36
Subtract 8
Ans-8
2 (x/6 +4) – 8
+8
28