Reviews Sheets
Do not try to do this in one night
A little bit everyday will help you get
it all in.
To Obtain
Kilometers
Meter
meters
centimeters
centimeters
Millimeter
millimeter
milliliters
Liters
liters
liters
liters
liters
liters
liters
liters
Imperial Gallon
Imperial Gallon
Imperial Gallon
Imperial Gallon
Imperial Gallon
Imperial Quart
Imperial Quart
Imperial Quart
Imperial Quart
Imperial Quart
To
to
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
Multiply
feet
inches
feet
inches
foot
Inch
foot
Fluid Ounces
pint
Cups
Quarts
Gallons
Imperial Ounce
Imperial Pint
Imperial Quart
Imperial Gallon
cup
ounce
pint
quart
gallon
cup
ounce
pint
quart
gallon
By
3280.8
39.37
3.28
0.393
0.032
0.039
0.003
0.034
2.11
4.227
1.056
0.264
0.219
1.759
0.879
0.219
19.215
153.721
9.607
4.803
1.201
4.803
38.43
2.4
1.2
0.3
To Obtain
feet
inches
feet
inches
foot
Inch
foot
Fluid Ounces
pint
Cups
Quarts
Gallons
Imperial Ounce
Imperial Pint
Imperial Quart
Imperial Gallon
cup
ounce
pint
quart
gallon
cup
ounce
pint
quart
gallon
To
to
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
kilometers
Meter
meters
centimeters
centimeters
Millimeter
millimeter
milliliters
Liters
liters
liters
liters
liters
liters
liters
liters
Imperial Gallon
Imperial Gallon
Imperial Gallon
Imperial Gallon
Imperial Gallon
Imperial Quart
Imperial Quart
Imperial Quart
Imperial Quart
Imperial Quart
by
0.305
2.5
30
25.4
29.573
0.473
0.946
3.785
0.568
1.137
4.546
1.201
1.201
imperial pint
imperial pint
imperial pint
imperial pint
imperial pint
Imperial Ounce
Imperial Ounce
Imperial Ounce
Imperial Ounce
Imperial Ounce
Kilogram
Kilogram
Gram
Gram
stone
stone
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
cup
ounce
pint
quart
gallon
cup
ounce
pint
quart
gallon
Ounce
pound
ounce
pound
ounce
pound
2.401
19.215
1.2
0.6
0.15
0.12
0.96
0.06
0.03
0.007
35.273
2.204
0.035
0.002
224
14
inches
inches
feet
yards
12
36
feet
feet
inches
yards
12
3
in-lb-pounds-force ninches
ft-lb-pounds-force feet
psi pounds per sq.in
Housepower hp
n-m newton meter
n-m newton meter
kilopascals kpa
kilowatts
0.113
1.356
6.895
0.354
cup
ounce
pint
quart
gallon
cup
ounce
pint
quart
gallon
Ounce
pound
ounce
pound
ounce
pound
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
To
imperial pint
imperial pint
imperial pint
imperial pint
imperial pint
Imperial Ounce
Imperial Ounce
Imperial Ounce
Imperial Ounce
Imperial Ounce
Kilogram
Kilogram
Gram
Gram
stone
stone
29.574
29..574
0.454
28.35
454
LENGTH X WIDTH
FLOOR SPACE
•
•
•
Area is surface measurement that has length and width or length and height but no
thickness.
Usually found by multiplying length by width or height. The answer is expressed in
square units.
Change both measurements to the same linear units before multiplying.
Example:
Area = length × width
A = 3” × 2”
A = 6 square inches
Example:
Volume = length × height × width
V = 3” × 2” × 2”
V = 12 cubic inches
N.A.A.R.S.O.
WALKING AROUND THE OUTSIDE WALL /EDGE .
What is a decimal?
WORD PROBLEMS
N.A.A.R.S.O.
21
Word problems
There are two steps to solving math word
problems:
• Translate the wording into a numeric equation
that combines smaller "expressions"
• Solve the equation!
N.A.A.R.S.O.
22
STRATEGIES FOR WORD PROBLEM
Word problems are a series of expressions that fits into
an equation
An equation is a combination of math expressions.
Suggestions:
Read the problem entirely
Get a feel for the whole problem
List information and the variables you identify
Attach units of measure to the variables (gallons, miles,
inches, etc.)
Define what answer you need,
as well as its units of measure
N.A.A.R.S.O.
23
Work in an organized manner
Working clearly will help you think clearly
Draw and label all graphs and pictures clearly
Note or explain each step of your process;
this will help you track variables and remember
their meanings
Look for the "key" words (above)
Certain words indicate certain mathematical
operations:
More vocabulary and key words:
"Per" means "divided by"
as "I drove 90 miles on three gallons of gas,
so I got 30 miles per gallon“
(Also 30 miles/gallon)
"a" sometimes means "divided by"
as in "When I tanked up,
I paid $3.90 for three gallons,
so the gas was 1.30 a gallon,
or $1.30/gallon
N.A.A.R.S.O.
25
"less than"
If you need to translate "1.5 less than x",
the temptation is to write "1.5 - x".
DON'T!
Put a "real world" situation in,
and you'll see how this is wrong:
"He makes $1.50 an hour less than me."
You do NOT figure his wage
by subtracting your wage from $1.50.
Instead,
you subtract $1.50 from your wage
"quotient/ratio of" constructions
If a problems says "the ratio of x and y",
it means
"x divided by y" or
x/y or
x÷y
"difference between/of" constructions
If the problem says
"the difference of x and y",
it means "x - y"
Problem Solving is easy if you follow
these steps
Understand
the
problem
N.A.A.R.S.O.
28
Step 1 – Understand the problem
Read the problem carefully.
Find the important information.
Write down the numbers.
Identify what the problem wants you
to solve.
• Ask if your answer is going to be a
larger or smaller number compared to
what you already know.
•
•
•
•
N.A.A.R.S.O.
29
Step 1 - Understand the Problem
Read the problem carefully.
• A Girl Scout troop went on a hike.
First they walked 1 mile east, then 2
miles south, then 3 miles west, and 1
mile north, then 2 miles east. How
far is the troop from their starting
point?
N.A.A.R.S.O.
30
Step 1 - Understand the Problem
Find the important information.
• A Girl Scout troop went on a hike.
First they walked 1 mile east, then
2 miles south, then 3 miles west,
and 1 mile north, then 2 miles east.
How far is the troop from their
starting point?
N.A.A.R.S.O.
31
Step 1 - Understand the Problem
Write down the key information.
• A Girl Scout troop went on a hike.
First they walked 1 mile east, then
2 miles south, then 3 miles west,
and 1 mile north, then 2 miles east.
How far is the troop from their
starting point?
N.A.A.R.S.O.
32
Step 1 - Understand the Problem
Write down the key information.
1 mile east,
2 miles south,
3 miles west,
1 mile north,
2 miles east
N.A.A.R.S.O.
33
Step 1 - Understand the Problem
Identify what the problem wants you
to solve.
•A Girl Scout troop went on a hike.
First they walked 1 mile east, then 2
miles south, then 3 miles west, and 1
mile north, then 2 miles east. How far
is the troop from their starting point?
N.A.A.R.S.O.
34
Problem Solving is easy if you follow
these steps
Decide how
you’re going
to
solve the
problem
N.A.A.R.S.O.
35
Step 2 - Decide how you’re going to
solve the problem
Choose a method
Use a graph
Write an equation
Find a pattern
Use reasoning
Make a table
Use formulas
Make a list
Work backwards
Draw a diagram
Act it out
N.A.A.R.S.O.
36
Step 2 - Decide how you’re going to
solve the problem
Make your diagram
W
start
N
S
E
finish
1 mile
N.A.A.R.S.O.
37
Problem Solving is easy if you follow
these steps
Solve
The
Problem
N.A.A.R.S.O.
38
Step 3 - Solve the problem
Measure the distance between the start
and the finish & compare it to the mile.
N
start
E
W
S
finish
1 mile
N.A.A.R.S.O.
39
Problem Solving is easy if you follow
these steps
Look
Back &
Check
N.A.A.R.S.O.
40
Step 4 - Look Back & Check
Reread the problem
• A Girl Scout troop went on a hike.
First they walked 1 mile east, then
2 miles south, then 3 miles west,
and 1 mile north, then 2 miles east.
How far is the troop from their
starting point?
N.A.A.R.S.O.
41
Step 4 - Look Back & Check
Compare the information from the
problem to your work.
N
1 mile east,
E
W
start
2 miles south,
S
3 miles west,
1 mile north,
2 miles east
finish
1 mile
N.A.A.R.S.O.
42
Step 4 - Look Back & Check
Did you solve what the problem
asked you to solve?
How far is the troop from their starting
point?
one mile
1 mile east,
N
start
2 miles south,
E
W
3 miles west,
S
finish
1 mile north,
1 mile
2 miles east
N.A.A.R.S.O.
43
1. Read the problem carefully.
2. Cross out unnecessary information.
3. Always show your work,
don't do it in your head.
4. Don't erase your mistakes,
cross out instead.
5. Draw a picture that illustrates the problem.
6. Reread your problem and check your
answers.
7. Write in your own words how you got your
answer.
John has 800 dollars in his checking account. He received from his
job a check for 1,200 dollars and deposit the amount in his checking
account. How much money does he have in his checking after the
deposit?
Solution
The fact of receiving money from his job is a gain.
Therefore, we need to perform addition
adding 1200 and 800
Total amount in checking account
= 800 + 1200
= 2000 dollars
Peter sells ice cream for a living. On Monday his revenue was 150
dollars. On Tuesday, his revenue was 100 dollars. Finally, on
Wednesday, his revenue was 50 dollars. How much is Peter's
revenue so far?
Solution
Peter is experiencing a gain in revenue. Therefore, we use
addition.
adding 150, 50 and 100
Peter's revenue = 150 + 50 + 100 = 300 dollars
Eiffel Tower is about 1063 feet high. The Statue of Liberty along
with its foundation and pedestal is about 305 feet. If you could
put the Statue of Liberty on top of the Eiffel Tower, how high up
in heaven will the two monuments reach?
Solution
The situation above is a combination of parts to form a whole.
Therefore, we use addition.
Adding 1063 and 305
Table of English linear measurement, also known as a conversion table.
1 foot
=
12 inches
1 yard
=
3 feet
1 yard
=
36 inches
1 mile
=
5,280 feet
1 mile
=
1,760 yards
FLUID VOLUME
OUNCES
CUP [ 8 ounces]
PINT [ 2 cups / 16 ounces]
QUART [2 pints /4 cups /32 ounces]
GALLON [4 quarts /8 pints /16 cups /128 ounces]
N.A.A.R.S.O.
INCHES TO MILLIMETERS INCHES TO CENTIMETERS
Convert the millimeter
measurement to inches by
dividing the millimeter figure
by 25.4.
For instance if the
measurement is
40 mm
you will divide this by 25.4.
eg.
40mm ÷25.4=1.574
N.A.A.R.S.O.
Convert the centimeter
measurement to inches by
dividing the centimeter figure
by 2.54.
For instance if the
measurement is
40 mm
you will divide this by 2.54.
eg.
40mm ÷2.54=15.74
CENTIMETER TO INCHES MILLIMETER TO INCHES
Convert the centimeter
measurement
to inches by multiplying the
centimeter figure by .0394.
For instance if the measurement is
250 Mm.
you will multiply this by .0394.
eg.
250 Mm x .0394 = 9.84 inches
.84 = 84/100 =42/50=21/25”
N.A.A.R.S.O.
Convert the millimeter
measurement
to inches by multiplying the
millimeter
figure by .0394.
For instance if the measurement
is
250 Cm
you will multiply this by .0394.
eg.
250 Cm x .0394 = 9.84 inches
.84 inches = 84/100
=42/50=21/25”
FEET TO METERS
Convert the
length[feet]measurement
to meters by multiplying the length
by .3048.
For instance if the length is
50’
you will multiply this by .3048.
eg.
50’ x .3048 = 15.29 meters
N.A.A.R.S.O.
METERS TO FEET
Convert the
length [meters]measurement
to meters by multiplying the length
by 3.281.
For instance if the length is
50’
you will multiply this by 3.281.
eg.
50 meters x 3.281 = 164.05 feet
POUNDS TO KILOGRAMS
KILOGRAMS TO POUNDS
Convert the pounds measurement to
kilograms by multiplying the weight by
2.205.
Convert the pounds measurement to
kilograms by multiplying the
weight by .45359.
For instance if the measurement is
50 lbs.
you will multiply this by .45359.
eg.
50 lbs. x .45359 = 22.67 kilograms
For instance if the measurement is 50 KG
you will multiply this by 2.205.
eg.
50KG x 2.205 = 110.25
N.A.A.R.S.O.
•
The metric system is used on all automobiles produced today.
•
A mechanic must be able to measure in metric as well as the English system.
•
In the center of the spectrum is unit.
•
Units in the metric system are meters, grams, and liters.
The following conversion table can be used to convert from the
metric system to the English system, or to convert from English
to metric.
Table of Linear Equivalents
1 inch
1 inch
1 inch
1 inch
=
=
=
=
0.0254 meter
0.254 decimeter
2.54 centimeters
25.40 millimeter
1 meter = 39.37 inches
1 decimeter = 3.937 inches
1 centimeter = 0.394 inch
1 millimeter = 0.03937 inch
1 foot = 0.3048 meter
1 yard = 0.9144 meter
N.A.A.R.S.O.
On this scale, the numbered divisions are centimeters (cm). The
unnumbered divisions are millimeters (mm). Ten millimeters
equal one centimeter.
3/4 inch
1 1/4 inches
1 7/8 inches
2 5/8 inches
3 1/8 inches
3 3/8 inches
N.A.A.R.S.O.
4
1/8 inches
4
1/2 inches
5
7/8 inches
TABLES HELP
N.A.A.R.S.O.
56
• Current has the symbol I and is
measured in amps (A)
• Resistance has the symbol R
)
and is measured in ohms (Ω
• Voltage has the symbol V and is
measured in volts(V)
• Current is measured with an
ammeter in series.
• Voltage is measured with a
voltmeter in parallel.
N.A.A.R.S.O.
If You know that P = 100 W, and V = 6 V. you can rearrange the equation to solve
for I and substitute in the numbers.
I = P/V = 100 W / 6 V = 16.66 amps
What would happen if you use a 12-volt battery and a 12-volt light bulb to get 100 watts of power?
100 W / 12 V = 8.33 amps
Ohm’s law is expressed in three statements:
1.
2.
3.
If voltage is increased, current flow is increased.
If voltage is decreased, current flow is decreased.
If resistance is increased, current flow is decreased.
The formula can be written in three ways:
E = I×R
where:
E = voltage (electromotive force)
I = current in amperes (inductance)
R = resistance in ohms
N.A.A.R.S.O.
E
I=
R
E
R=
I
N.A.A.R.S.O.
English vs. Metric Units
Which is longer?
A. 1 mile or 1 kilometer
B. 1 yard or 1 meter
1 mile
1.6 kilometers
C. 1 inch or 1 centimeter
1 inch = 2.54 centimeters
1 yard = 0.9444 meters
Left Image: http://webapps.lsa.umich.edu/physics/demolab/controls/imagedemosm.aspx?picid=1167
Right Image: http://share.lancealan.com/N800%20ruler.jpg
English vs. Metric Units
Which is larger?
1 fl oz = 29.573 ml
A. 1 liter or 1 gallon
1 12-oz can of soda
would equal
approximately 355 ml.
B. 1 liter or 1 quart
C. 1 milliliter or 1 fluid ounce
1 quart = 0.946 liters
1 gallon = 3.79 liters
It would take approximately 3 ¾
1-liter bottles to equal a gallon.
Micrometer Reading
To read the English micrometer:
Step 1. Read the highest number showing on the barrel.
Step 2. Add 0.025” for each full vertical space showing.
Step 3. Add the number on the sleeve that lines up with the
horizontal line on the barrel.
The reading is the sum.
Example:
Caution: Do not read this space as full until the zero is lined up
with the horizontal line on the barrel.
To read this metric micrometer setting:
Step 1. Read the number of full divisions on the barrel. 10.00
Step 2. Add the 0.5-mm divisions
0.50
Step 3. Add the thimble reading.
0.10
The reading is the sum.
10.60 mm
0.240
0.425
0.800
0.980
0.599
0.626