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If you have a mathematical question to answer,
you can do it all yourself, or you can let AutoMathic help you do
it! With AutoMathic, you focus on specifying the problem, and let the computer do the mechanical work of solving it! 
The documentation has lots of examples throughout the main body, in the quickreferences, and in the lexicon... The examples were chosen to demonstrate not only AutoMathic's vocabulary, but also a wide range of its grammar and default knowledge. By seeing examples of its language in an understandable context, the user should begin to learn AutoMathic's "dialect" of English in the same way they might learn a foreign language by being immersed in it. 
General Math
Numbers and Numeric ConstantsUnits and Unit Conversion
Arithmetic Expressions
Algebraic Equations
Percentages
Money
Circles
Simple UnitsPhysics & Chemistry
Compound Units
Multidimensional Units
You enter... 
AutoMathic understands... 
Two 
2 
Two pair 
4 
0.125 
0.125
(or
1 / 8) 
A thousand 
1,000 
Seven trillion 
7,000,000,000,000 
Tens 
10 
100's 
100 
A sixteenth 
0.0625
(or
1 / 16) 
Two thirds 
0.666666666666667
(or
2 / 3) 
Four tenths 
0.4 (or 2 / 5) 
8 billionths 
0.000000008 
Three baker's dozens 
39 
6 gross 
864 
Pi 
3.14159 
Tau 
6.28318 
e 
2.71828 
Golden ratio 
1.61803 
Avogadro's number 
602,200,000,000,000,000,000,000 
You enter... 
AutoMathic understands... 
Three Pi over two 
4.712385 
Twice the length added to
twice the width 
2 l +
2 w 
Twice the sum of the length
and the width 
2 ( l + w ) 
3x the diameter 
3 d 
Half the mass 
m / 2 
A third of the sum of cost
and tip 
( c +
t ) / 3 
The ratio of width to height 
w / h 
The cost without half the
taxes 
c  t / 2 
You enter... 
AutoMathic understands... 
Twice the sum of the width and the length is the perimeter.  2 (l + w) = p 
The area would be half the base times the height.  b h a =  2 
How much less than e is Pi over two? 
3.14159 2.71828  a =  2 1.147485 is THE ANSWER. 
Half of what age is three more than a fourth of itself?  a a  = 3 +  2 4 12 is THE AGE. 
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AutoMathic understands... 
12% of 275 million 
12
 275 (1000000) 100 33,000,000 is 12 % OF 275 MILLION. 
8.25 percent more than 198 
/
8.25\ ( 1 +  ) 198 \ 100 / 214.335 is 8.25 % MORE THAN 198. 
12 pct less than 224.99 
/ 3 \ 224.99 ( 1   ) \ 25/ 197.9912 is 12 % LESS THAN 224.99. 
5% of each donation is overhead  d  = o 20 
How many millions is 12% of
275 million? 
1000000 n = 33000000 33 is THE NUMBER. 
What percentage of fifty is thirty?  p
 (50) = 30 100 60 is THE PERCENTAGE. 
Two dozen makes up only 20% of what total? 
20
12 (2) =  t 100 t 24 =  5 120 is THE TOTAL. 
What percent is one seventh?  a 1  =  100 7 14.2857142857143 (or 100 / 7, or 14 & 2 / 7) is THE ANSWER. 
Seventy percent is the ratio of successes to attempts.  7 s  =  10 a 
Thirty is a dozen less than 97% of what age?  97 a 30 =   12 100 43.298969072165 is THE AGE. 
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AutoMathic understands... 
What percentage of a cost are its taxes?  (Find p) c p  = t 100 7.62124711316397 is THE PERCENTAGE. 
What must the price have been assuming that tips were 2.75?  (Find p) T = 2.75 16.9361046959199 is THE PRICE. 
The price is 12% off of what when the cost is 225?  (Find
a) / 3 \ p = ( 1   ) a \ 25/ c = 225 236.195674994751 is THE AMOUNT. 
The price consists of 0.65 per apple and 1.25 per drink.  p =
0.65 a + 1.25 d 
The price for each tire is 79.95. Find the cost for 5 tires.  p  = 79.95 t (Find 5c/t) 432.729375 is THE COST FOR 5 TIRES. 
Find the price such that the cost is 225.  (Find
p) C = 225 207.852193995381 is THE PRICE. 
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AutoMathic understands... 
The circumference is how many
times the radius? 
c = n
r c = 2 (3.14159) r 6.28318 is THE NUMBER. 
21 is the difference between
what circumference and what radius? 
(Find
r) (Find c) 21 = c  r c = 2 (3.14159) r 24.9748787661976 is THE CIRCUMFERENCE. 3.97487876619763 is THE RADIUS. 
Compute the circumference
where the diameter is 13. 
(Find c) d = 13 d = 2 r c = 2 (3.14159) r 40.84067 is THE CIRCUMFERENCE. 
When the radius is 3, how
much more than that's the circumference? 
r = 3 (Find a) a + r = c c = 2 (3.14159) r 15.84954 is THE ANSWER. 
Category 
Builtin Units
(not including abbreviations) 
Length 
millimeters, centimeters, inches, feet, meters, yards, fathoms, furlongs, kilometers, miles, nautical miles, leagues, microns / micrometers, nanometers, angstroms, astronomical units, light years, parsecs 
Time 
nanoseconds, microseconds, milliseconds, seconds, minutes, hours, days, weeks, fortnights, months, years, decades, centuries, millenia 
Weight & Mass 
ounces, pounds, tons, milligrams, grams, kilograms, AMU, metric tons, kilotons 
Liquid / Volume 
teaspoons, tablespoons, fluid ounces, cups, pints, quarts, gallons, milliliters, liters, drops 
Temperature 
Fahrenheit, Celsius / Centigrade, Kelvin 
Pressure 
atmospheres, psi, torr, inches of mercury, millimeters of mercury, pascals, kilopascals, bars, millibars 
Frequency 
hertz, kilohertz, megahertz, gigahertz 
Clock & Calendar
Frequency 
hourly, daily, weekly, monthly, quarterly, yearly, etc. 
Angular 
radians, degrees, gradians, grads, right angles, revolutions, rotations, circles, arcminutes, arcseconds 
Information Storage 
bits, nibbles, bytes, words, longwords, kilobytes, megabytes, gigabytes, terabytes, petabytes, kilobits, megabits, gigabits 
Electrical 
amperes, milliamperes,
coulombs, volts, farads, microfarads, picofarads 
You enter... 
AutoMathic understands... 
Inches per meter? 
(Find
i/m) 39.3700787401575 is INCHES PER METER. 
Seconds in 1.5 hrs 
(Find
1.5s/h) 5,400 is SECONDS IN 1.5 HRS. 
What's 165[lb] in terms of
[kg's]? 
(Find 165k/p) 75 is 165 [ LB ] IN TERMS OF [ KG'S ]. 
How many unit cc's is 5 unit
pints? 
n
5  =  m P 2,365.625 is THE NUMBER. 
The temperature measured in
degrees F is 78. What's the temperature in terms of Kelvin? 
f t =
78 (Find kt) 298.715555555556 is THE TEMPERATURE IN TERMS OF KELVIN. 
Convert 90[PSI] into [mmHg]. 
(Find
90t/p) 4,653.0612244898 is CONVERT 90 [ PSI ] INTO [ MMHG ]. 
How many times 2.4[mHz] is
3.1[gHz]? 
2.4 n 3.1  =  m g 1,291.66666666667 is THE NUMBER. 
Find the cost daily when the
cost semiannually is 475. 
(Find c/d) c  = 475 s 2.6009582477755 is THE COST DAILY. 
How many [deg's] is 1.5 pi
[radians]? 
n 1.5 (3.14159)  =  d r 270 is THE NUMBER. 
What percentage of 54[mb] is
24[kb]? 
27 p 24  =  50 m k 0.0434027777777778 (or 25 / 576) is THE PERCENTAGE. 
Category 
Component Units 
Builtin Units
and Constants (including some abbreviations) 
Speed 
length /
time 
miles per hour (MPH),
kilometers per hour (KPH), feet per second (FPS), meters per
second (MPS), knots, speed of sound (mach _), speed of light
(_ C) 
Angular Velocity 
angle /
time 
revolutions per minute (RPM) 
Acceleration 
speed /
time 
G's, Gees, G forces, etc. 
Momentum 
mass x
speed 

Force 
mass x acceleration  newtons (N) 
Density 
mass /
volume 
density of water, mercury,
alcohol, gasoline, air, helium, carbon dioxide, steam,
aluminum, iron, steel, copper, lead, gold 
Concentration 
number /
volume 
moles per liter (_ molar) 
Energy, Work, Torque 
force x
length 
joules (J), kilojoules (kJ),
calories (cal), food calories / kilocalories (kcal), watt
hours (Wh), kilowatt hours (kWh), British thermal units
(BTUs) 
Power 
energy /
time 
watts (W), kilowatts (kW),
horsepower (HP) 
Specific Heat 
energy /
mass 
specific heat of water, ice,
steam, mercury, alcohol, aluminum, copper, glass, iron,
steel, lead, wood, flesh 
Fuel Efficiency 
length /
volume 
miles per gallon (MPG) 
Bandwidth 
storage /
time 
You enter... 
AutoMathic understands... 
The speed is 65[mph]. How many [kph] is a third of the speed? 
65
h s =  m n h s  =  k 3 34.86912 is THE NUMBER. 
What's 55[mph] in terms of
[furlongs/fortnight]? 
(Find 55fh/(mF)) 147,840 is 55 [ MPH ] IN TERMS OF [ FURLONGS / FORTNIGHT ]. 
3[drops/sec] converts to how
many [gallons/day]? 
3
s n D  =  d g 3.42404227212682 is THE NUMBER. 
Convert 1.3[gm/cc] into
[lb/gal]. 
(Find 1.3mp/(gG)) 10.8251 is CONVERT 1.3 [ GM / CC ] INTO [ LB / GAL ]. 
How many times 5[km/l] is
23[mpg]? 
5 l
n 23 g  =  k m 1.95587381770145 is THE NUMBER. 
How many unit MB'S is 196[kilobits/sec] x 3.5[min]?  n 686 s  =  m M k 4.90665435791016 is THE NUMBER. 
There are 42 gallons a
barrel. How many [gallons/sec] does 35,000[barrels/day] convert to? 
g 42 =  b n s 35000 d  =  g b 17.0138888888889 is THE NUMBER. 
Category 
Component Units 
Builtin Units
(including some abbreviations) 
Area 
length_{1}
x length_{2} length squared length sqrd length sqr length sq length ^ 2 
acres (ac), sections,
hectares (ha) 
Area 
length2 
inch2 (in2), foot2 (ft2),
yard2 (yd2), mile2 (mi2), nautical mile2 (nmi2) inches2 (ins2), feet2 (ft2), yards2 (yds2), miles2 (mis2), nautical miles2 (nmis2) millimeter2 (mm2), centimeter2 (cm2), meter2 (m2), kilometer2 (km2) millimeters2 (mms2), centimeters2 (cms2), meters2 (ms2), kilometers2 (kms2) 
Volume 
length_{1} x length_{2} x length_{3} length cubed length cbd length ^ 3 
teaspoons, tablespoons, fluid ounces, cups, pints, quarts, gallons, milliliters, liters, drops 
Volume 
length3 
inch3 (in3), foot3 (ft3),
yard3 (yd3), mile3 (mi3), nautical mile3 (nmi3) inches3 (ins3), feet3 (ft3), yards3 (yds3), miles3 (mis3), nautical miles3 (nmis3) millimeter3 (mm3), centimeter3 (cm3), meter3 (m3), kilometer3 (km3) millimeters3 (mms3), centimeters3 (cms3), meters3 (ms3), kilometers3 (kms3) 
Time^{2} 
time_{1}
x time_{2} time squared time sqrd time sqr time sq time ^ 2 

Time^{2} 
time2 
second2 (sec2, s2), seconds2 (secs2) 
Time^{3} 
time_{1}
x time_{2} x time_{3} time cubed time cbd time ^ 3 

Time^{3} 
time3 
second3 (sec3, s3), seconds3 (secs3) 
Other^{2} 
unit_{1}
x unit_{2} unit squared unit sqrd unit sqr unit sq unit ^ 2 

Other^{3} 
unit_{1}
x unit_{2} x unit_{3} unit cubed unit cbd unit ^ 3 

Other^{N} 
unit_{1} x unit_{2} x ... x unit_{N} 
You enter... 
AutoMathic understands... 
If the area is 5x7[in^2], what's the area in [cm2]? 
35 a =  i i (Find acc) 225.806 is THE AREA IN [ CM2 ]. 
What's 350[in cubed] in terms of [cm^3]? What's 350[in cubed] measured in gallons? 
(Find 350ccc/(iii)) (Find 350g/(iii)) 5,735.4724 is 350 [ IN CUBED ] IN TERMS OF [ CM ^ 3 ]. 1.51531635402906 is 350 [ IN CUBED ] MEASURED IN GALLONS. 
Convert 8[ft] by 3[ft] by 7[ft] into [meters^3]. 
(Find 168mmm/(fff)) 4.757230227456 is CONVERT 8 [ FT ] BY 3 [ FT ] BY 7 [ FT ] INTO [ METERS ^ 3 ]. 
3,000[ft squared] is 40[ft] times how many unit yards? 
3000
40 n  =  f f f y 3000 40 n  =  f y 25 is THE NUMBER. 
How many [ft sq] is 2x6[m^2]? 
n
12  =  f f m m 129.1669250000517 is THE NUMBER. 
What percentage of 1[meter cubed] is 4[in] x 6[in] x 8[in]? 
p 192  =  100 m m m i i i 0.3146316288 is THE PERCENTAGE. 
How many times 2[ft cubed] is 2[in] x 1[m] x 25[ft]?  2
n 50  =  f f f f i m 2 n 50  =  f f i m 6.83508311461067 is THE NUMBER. 
How many [feet/(second^2)] is 5.5 Gee?  n s s
5.5 (9.8) s s  =  f m n 5.5 (9.8)  =  f m 176.837270341207 is THE NUMBER. 
You enter... 
If the average speed is 130[mph], and the time is 73[sec], find the distance measured in kilometers. 
AutoMathic understands... 
Let 'A' stand for "AVERAGE SPEED"

You enter... 
How many Gees is the acceleration if the speed was 60[mph], and the time was 3.4[sec]? 
AutoMathic understands... 
Let 'N' stand for "NUMBER"

You enter... 
Given that the distance is a quarter of a unit mile, and the time is 5.6[sec], find the speed measured in mph. 
AutoMathic understands... 
Let 'D' stand for "DISTANCE"

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Find the mass measured in lbs so that the force is 750[N] when acceleration is 1 Gee. 
AutoMathic understands... 
Let 'M' stand for "MASS"

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If the average speed is 50[kph], and the radius is 50[m], how many G's would the centripetal acceleration be? 
AutoMathic understands... 
Let 'A' stand for "AVERAGE SPEED"

You enter... 
How many unit Joules is the work when the mass is 15[kg], acceleration is 1 G, and distance is 12[m]? 
AutoMathic understands... 
Let 'N' stand for "NUMBER"

You enter... 
How many unit Joules is the KE given that the average speed is 8.9[m/s], and the mass is 70[kg]? 
AutoMathic understands... 
Let 'N' stand for "NUMBER"

You enter... 
If the mass is 2,200[lb], and the height is 25[m], how many unit kJ's is the potential energy? 
AutoMathic understands... 
Let 'M' stand for "MASS"

You enter... 
How many unit kW would the power be assuming the energy is potential energy, mass is 160[lb], height was 4.5[m], and the time was 4[sec]? 
AutoMathic understands... 
Let 'N' stand for "NUMBER"

You enter... 
If the momentum was 2,500[lb] x 65[mph], what would the speed in [mph] be if the mass were only 200[lb]? 
AutoMathic understands... 
Let 'M' stand for "MOMENTUM"

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Calculate the torque in [N*m] when the radius is 18[cm], the mass is 132[lb], and acceleration is 1 G. 
AutoMathic understands... 
Let 'T' stand for "TORQUE"

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Find the spring constant in [N/m] given that the mass is 200[kg], and the displacement is 3[cm]. Acceleration is 1 G. 
AutoMathic understands... 
Let 'S' stand for "SPRING CONSTANT"

You enter... 
If the wave speed is the speed of sound, and the frequency is F#, how many unit inches long is the wavelength? 
AutoMathic understands... 
Let 'W' stand for "WAVE SPEED"

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If the length is 36[inches], and the overtone is two, how many unit cm long is the wavelength? 
AutoMathic understands... 
Let 'L' stand for "LENGTH"

You enter... 
Find the doppler shift in unit Hz. The wave speed is mach 1, the frequency is G natural, and the relative speed is 45[mph]. 
AutoMathic understands... 
Let 'D' stand for "DOPPLER SHIFT"

You enter... 
How many trillionths of a unit Coulomb is the charge when the capacitance is 53[pF], and the voltage is 12[V]? 
AutoMathic understands... 
Let 'N' stand for "NUMBER"

You enter... 
Calculate the charge measured in Coulombs when the current is 2.5[amps], and the time is 4[min]. 
AutoMathic understands... 
Let 'C' stand for "CHARGE"

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Given that voltage is 6[V], and the current is 300[mA], find the resistance measured in ohms. 
AutoMathic understands... 
Let 'V' stand for "VOLTAGE"

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If the power is 40[W], and the voltage is 12[V], find the resistance measured in ohms, and the current measured in amps. 
AutoMathic understands... 
Let 'P' stand for "POWER"

You enter... 
If the current is 15[Amps] when the voltage is 120[V], find the electrical energy in [kWh] when the time is 90[hr's]. 
AutoMathic understands... 
Let 'C' stand for "CURRENT"

You enter... 
Find the mass per particle measured in amu, when the mass for 6 moles is 84[gm]. 
AutoMathic understands... 
Let 'M' stand for "MASS"

You enter... 
If the formula weight is 106, find the number of grams such that the molar concentration is 4 when the number of ml is 1,500. 
AutoMathic understands... 
Let 'F' stand for "FORMULA WEIGHT"

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If the density is half the density of steel, and 75% of the volume is 2[gal], find the mass measured in pounds. 
AutoMathic understands... 
Let 'D' stand for "DENSITY"

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If the specific gravity is 0.668, find the density measured in lb/gal. 
AutoMathic understands... 
Let 'S' stand for "SPECIFIC GRAVITY"

You enter... 
Find the number of nucleons, and the atomic weight. The atomic number is 6, the ratio of protons to neutrons is 1:1, and the ionic charge is +2. 
AutoMathic understands... 
Let 'N' stand for "NUCLEONS"

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Compute the volume measured in liters, if the number of moles is 1, pressure is standard pressure, and temperature is standard temperature. 
AutoMathic understands... 
Let 'V' stand for "VOLUME"

You enter... 
Calculate the heat energy in [J] when the number of moles is 5, and the temperature is room temperature. 
AutoMathic understands... 
Let 'H' stand for "HEAT ENERGY" 
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Find the heat energy measured in Joules given that the mass is 7.05[gm], deltaT is 75, and the specific heat is the specific heat of iron. 
AutoMathic understands... 
Let 'H' stand for "HEAT ENERGY"

You enter... 
What's the heat capacity in [kJ] when the volume is 4[L], the density is the density of water, and the specific heat is the specific heat of water? 
AutoMathic understands... 
Let 'H' stand for "HEAT CAPACITY"
