219 results for “ip”
Multiply numerators and denominators straight across.
Divide by multiplying by the reciprocal (flip and multiply).
Two equal ratios; solve using cross multiplication.
Parentheses, Exponents, Multiply/Divide, Add/Subtract.
Gratuity as a percentage of the bill.
The multiplicative inverse of a number.
A number multiplied by itself.
A number multiplied by itself three times.
Multiplying powers with the same base adds the exponents.
Raising a power to a power multiplies the exponents.
Multiply two binomials: First, Outer, Inner, Last.
A negative exponent means reciprocal.
Reciprocal of the average of reciprocals.
A negative exponent gives the reciprocal.
Area enclosed by an ellipse.
Secant and cosecant as reciprocals.
Reciprocal of cosine.
Reciprocal of sine.
Reciprocal of tangent.
Constants factor out of a derivative.
Antiderivative of the reciprocal function.
Measures how two variables vary together.
Probability of both independent events occurring.
If n items go into k containers, some container holds at least this many.
Multiply every entry of a matrix by a scalar.
The identity matrix leaves any matrix unchanged under multiplication.
Volume of the parallelepiped spanned by three vectors.
Multiplying by the identity leaves a matrix unchanged.
Power dissipated in an electrical component.
Force needed to keep an object in circular motion.
Inward force needed for circular motion.
Buoyant force equals the weight of fluid displaced.
Faster-moving fluid has lower pressure (energy conservation in flow).
Planets orbit the Sun in ellipses with the Sun at one focus.
Position and momentum cannot both be known with unlimited precision.
Buoyant force equals the weight of displaced fluid.
Pressure applied to a confined fluid transmits undiminished.
Buoyant force equals weight of displaced fluid.
Laminar flow rate through a pipe.
Limit on knowing position and momentum together.
Power dissipated by a component.
Reciprocals of parallel resistances add.
Reciprocals of series capacitances add.
Relationship between acidity and basicity at 25°C.
Fat-distribution health indicator.
Body-shape ratio linked to health risk.
Every ingredient expressed relative to flour weight — the backbone of bread recipes.
Rescale each ingredient for a different number of servings.
Total recipe cost divided across the number of servings.
Total fuel needed is the fuel-burn rate multiplied by flight time.
Latest date a deferred defect must be fixed: the discovery date plus the Minimum Equipment List category interval. The day of discovery is “day zero” and is not counted.
Total drag coefficient is the sum of parasite drag and lift-induced drag — the fundamental performance relationship for an airframe.
Thrust horsepower is the engine's brake horsepower multiplied by propeller efficiency — the power actually converted to thrust.
Interest earned on principal at a simple rate.
Value of principal compounded n times per year.
The total profit expected from a customer over the whole relationship.
How much total output rises from an initial change in spending.
Total impact of spending given marginal consumption.
Flip a quoted rate to express it from the other currency’s point of view.
The monetary value of a one-pip move for a given trade size.
Gratuity based on a bill amount.
Total fuel cost for a trip.
Adjust ingredient quantities for a different number of servings.
Per-person share of a bill including tip.
A repeating event's period is the reciprocal of its frequency.
Least common multiple via the greatest common divisor.
How efficiently a data centre uses energy, versus overhead like cooling.
Frequency shift of an echo from a moving target; the factor of two accounts for the round trip to the target and back.
Overall positioning error is the geometry factor (dilution of precision) multiplied by the per-satellite ranging error.
Total revenue is the selling price multiplied by the number of units sold.
Annual recurring revenue annualises the monthly recurring revenue of a subscription business.
Overtones of a note are whole-number multiples of the fundamental.
Frequency is the reciprocal of the wave's period.
Lowest note of a pipe open at both ends (like a flute).
Bitwise XOR of message and key; XOR again with k to decrypt.
A good hash flips about half its output bits when one input bit changes.
Shift each letter forward by k positions.
Aperture, shutter and ISO trade off to keep exposure constant.
Energy that brakes must dissipate to stop a moving car.
A floating ship displaces its own weight in water.
Depth of hull below waterline from displacement and waterplane area.
Stability measure; positive GM means the ship rights itself.
Fuel burn rises with the cube of speed for a ship.
Max purchase price for a flip using the 70% rule.
Every ingredient expressed relative to the flour weight — the backbone of bread recipes.
Scales every ingredient up or down for a different number of servings.
Single multiplier applied across a whole recipe when changing batch size.
Share of customer demand met immediately from stock.
Total shipment cost spread across the units delivered.
How long a shipment or container sits idle at a facility.
Reduction in a steel pipe string's weight when submerged in drilling mud.
Mud volume per minute from a triplex pump's bore, stroke and speed.
Volume of oil originally in a reservoir (in stock-tank barrels).
Percentage of oil in place that can actually be produced.
Internal volume of pipe per foot of length (barrels per foot).
Fraction of annular velocity effectively lifting cuttings out of the hole.
Area under an irregular boundary using parabolic strips.
Area under a boundary by summing trapezoidal strips.
Number of usable IPv4 addresses in a subnet with an n-bit prefix.
Predicted total revenue a single customer will generate over their relationship with a business.
Flips |0⟩ to |1⟩ and vice versa — the quantum equivalent of a classical NOT gate.
Two-qubit gate that flips the target qubit only when the control qubit is |1⟩.
Drops per minute to deliver a given volume over a set time via IV drip.
In a closed system, matter is neither created nor destroyed — the total mass before a reaction equals the total mass after.
A given chemical compound always contains its component elements in the same fixed ratio by mass, regardless of source.
When two elements form more than one compound, the masses of one element combining with a fixed mass of the other are in ratios of small whole numbers.
The total pressure of a mixture of non-reacting gases equals the sum of the partial pressures each gas would exert alone.
The rate at which a gas effuses through a tiny hole is inversely proportional to the square root of its molar mass.
At the same temperature and pressure, equal volumes of gases contain equal numbers of molecules — so volume is proportional to moles.
The vapour pressure of a solvent above a solution equals its mole fraction times the pure solvent's vapour pressure.
The concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid.
When a system at equilibrium is disturbed by a change in concentration, temperature or pressure, it shifts to partially counteract the change.
The mass of substance deposited or dissolved at an electrode is proportional to the electric charge passed through the cell.
The rate at which an object cools is proportional to the temperature difference between the object and its surroundings.
The diffusion flux of particles flows from regions of high concentration to low, proportional to the concentration gradient.
X-rays reflected from parallel crystal planes interfere constructively when the path difference is a whole number of wavelengths.
The magnetization of a paramagnetic material is proportional to the applied magnetic field and inversely proportional to absolute temperature.
Gives the magnetic field produced at a point by a small element of current-carrying wire.
The heat generated by an electric current in a conductor is proportional to the square of the current, the resistance and the time.
The speed of fluid flowing out of an opening equals the speed it would reach falling freely from the height of the fluid surface.
For metals, the ratio of thermal conductivity to electrical conductivity is proportional to absolute temperature, with a nearly universal constant.
A Vedic sutra for multiplying numbers close to a base (10, 100, 1000, etc.). Works by finding how far each number is from the base.
A general Vedic multiplication method that works for any two numbers. Uses vertical and crosswise multiplication patterns.
Instantly square any number ending in 5. Multiply the tens digit by (tens digit + 1), then append 25.
Instantly multiply any two-digit number by 11 by splitting and adding the digits.
x% of y = y% of x. When one direction is hard, flip it! This works because (x/100)×y = (y/100)×x.
Multiply by 10 and divide by 2 (or vice versa) for instant results.
Split large multiplications into simpler parts using the distributive property.
A quick way to verify multiplication and addition results by checking digit sums modulo 9.
Multiplying any number by a string of nines is instant: subtract 1 from the number for the left part, then take the complement for the right part.
When numbers are near a convenient working base that is a multiple of a power of 10, use a proportional base to simplify the multiplication.
Multiply by 10 and subtract the original number — much faster than multiplying by 9 directly.
Since 25 = 100 ÷ 4, multiply by 100 and divide by 4 for instant results.
Multiply by 10, then add half of that — because 15 = 10 + 5 and 5 is half of 10.
When one factor is even, halve it and double the other to reach an easier multiplication.
For numbers a little above 100, use the surplus from 100 to multiply almost instantly.
Multiplying by 4 is doubling twice; by 8 is doubling three times. No memorised tables needed.
Multiply two binomials by combining First, Outer, Inner, Last terms.
Two numbers equally spaced around a middle value m multiply to m² − d², using the difference of squares.
Find 10% first, then build 15% or 20% from it in your head.
Multiply miles by 1.6 for km, or divide km by 1.6 for miles. Consecutive Fibonacci numbers are handy approximations.
Instantly multiply two numbers that share the same tens digit and whose units digits add up to 10 (e.g. 43 × 47, 62 × 68).
Any two-digit number times 101 is simply the number written twice — no working needed.
Multiplying by 50 is the same as multiplying by 100 and halving — both easy steps.
Multiply by 12 by using the easy ×10 and then adding twice the number — the same idea extends to 13 and 14.
Add up 2 + 4 + 6 + … up to the Nth even number instantly with a single multiplication.
Extend the ×11 trick to three-digit numbers by adding each neighbouring pair of digits.
Multiply any two numbers from 11 to 19 in your head with a quick three-step pattern.
Multiply two numbers close to 1000 using their deficits from the base, just like the near-100 trick.
Reverse the digits of any two-digit number and subtract — the result is always 9 times the difference of the digits.
Since 125 = 1000 ÷ 8, multiplying by 125 is just adding three zeros and dividing by 8.
Since 75 = 3 × 25, multiply by 3 and then by 25 (which is ×100 ÷ 4).
Multiplying by 1.5 is simply adding half of the number to itself — handy for recipes and time-and-a-half pay.
Builders use multiples of the 3-4-5 triangle to mark a perfect right angle — no protractor needed.
Multiply any number by a repunit of 9s (99, 999, 9999…). Split the answer into two halves: left half = number − 1, right half = complement of left half to all 9s.
The general Vedic sutra for multiplying any two numbers. Work digit by digit: units × units, then cross-multiply, then tens × tens — carrying as needed.
Verify any multiplication by checking digital roots. The digital root of the product must equal the digital root of (digital root of factor 1 × digital root of factor 2).
When two numbers are equidistant from a round "anchor" number, use the difference-of-squares identity: (anchor + d)(anchor − d) = anchor² − d².
Compare two fractions without finding a common denominator. Cross-multiply: if a/b vs c/d, compare a×d with c×b.
Multiply by rounding one factor to the nearest easy number, then adjusting. For example, 48 × 7 = 50 × 7 − 2 × 7.
Square any number by rounding to the nearest multiple of 10: n² = (n+d)(n−d) + d², where d is the distance to that multiple.
Multiply any number by 99 using: n × 99 = n × 100 − n. Just append two zeros and subtract the original number.
Multiply a two-digit number by 111: n × 111 = n × 100 + n × 11. Use the multiply-by-11 trick for the second part.
Since 37 × 3 = 111, multiply by 37 by first dividing the other number by 3, then multiplying by 111. Works perfectly when the number is divisible by 3.
Dividing by 25 = multiplying by 4 then dividing by 100. Much simpler for mental math since multiplying by 4 (double twice) is easy.
To square any number ending in 5: multiply the tens digit by (tens digit + 1), then append 25. Works instantly for any size.
When both numbers are close to 100, use their deficits: cross-subtract to get the hundreds, multiply deficits for the units.
Multiple successive discounts are NOT additive. Multiply the remaining fractions: 20% off then 10% off = 0.8 × 0.9 = 0.72, meaning 28% total discount (not 30%).
When raising an exponent to another power, multiply the exponents: (aᵐ)ⁿ = aᵐˣⁿ. Simplifies nested exponents instantly.
Apply successive discounts by multiplying the "keep" fractions, not by adding the percentages. The result is always less than the sum of discounts.
To find how many years it takes for money to TRIPLE at a given interest rate, divide 114 by the rate. Like the Rule of 72 but for tripling.
Fuel cost = (distance ÷ fuel efficiency) × price per litre. Know your car does and estimate trips in seconds.
Scale any recipe by multiplying each ingredient by (desired servings ÷ original servings). Works for any ratio.
Multiply any number by 6 by first multiplying by 3 (easy), then doubling the result. Two simple steps instead of one hard one.
Multiply by 3 by doubling the number and adding the original once more.
Multiply by 7 by multiplying by 8 (triple-double) and subtracting the original: 7n = 8n − n.
Split 13 into 10 + 3: multiply by 10, then add three times the number.
Split 14 into 10 + 4: multiply by 10, then add four times the number.
Since 16 = 2⁴, multiply by 16 by doubling the number four times in a row.
Use 35 = 70 ÷ 2: multiply by 70, then halve.
Use 45 = 90 ÷ 2: multiply by 90, then halve.
Use 55 = 110 ÷ 2: multiply by 110, then halve.
Use 65 = 130 ÷ 2: multiply by 130, then halve.
Use 85 = 170 ÷ 2: multiply by 170, then halve.
Use 95 = 100 − 5: multiply by 100, then subtract five times the number.
Use 105 = 100 + 5: multiply by 100, then add five times the number.
Use 110 = 100 + 10: multiply by 100, then add ten times the number.
Any 3-digit number × 1001 just repeats itself: abc × 1001 = abcabc.
Use 250 = 1000 ÷ 4: multiply by 1000, then divide by 4.
Use 500 = 1000 ÷ 2: multiply by 1000, then halve.
Use 2.5 = 10 ÷ 4: multiply by 10, then divide by 4.
Use 7.5 = 15 ÷ 2 = 30 ÷ 4: multiply by 30, then divide by 4.
Multiplying by 0.5 is the same as halving the number.
Multiplying by 0.25 is the same as dividing by 4 (halve twice).
Use 15 = 30 ÷ 2: multiply by 2, then divide by 30 — or divide by 3 then by 5.
Use 50 = 100 ÷ 2: multiply by 2, then divide by 100.
Use 125 = 1000 ÷ 8: multiply by 8, then divide by 1000.
Use 250 = 1000 ÷ 4: multiply by 4, then divide by 1000.
Find 1% by moving the decimal two places, then multiply up to any percentage you need.
Use the distributive law: split one factor into easy parts, multiply each, then add.
Estimate 1 ÷ n by finding how many times n fits into a convenient power of 10.
When multiplying, double one factor and halve the other to reach an easier pair — the product stays the same.
To find a fraction of a number, divide by the denominator, then multiply by the numerator.
Round both numbers to multiples of ten, multiply, then subtract the cross-correction for a close estimate.
When numbers are close, multiply one by the count and adjust by the small differences from it.
If a/b = c/x, cross-multiply to get a×x = b×c, then solve for x.
When two fractions are equal, cross-multiply to clear denominators in one step.
Multiply kilograms by 2.2 to get pounds (close enough for daily use).
Multiply inches by 2.54 to get centimetres.
Divide centimetres by 2.54 to get inches (or multiply by 0.39).
Multiply metres by 3.28 to get feet.
One US cup ≈ 240 ml. Multiply cups by 240.
Interest = Principal × Rate × Time (rate as a decimal, time in years).
Each year multiply by (1 + rate). Over a few years, chain the multipliers.
Selling price = cost × (1 + markup%). A 40% markup means multiply cost by 1.4.
Area = length × width. Multiply the two sides for square footage/metres.
Average speed over equal distances is the harmonic mean: 2ab ÷ (a + b), not the plain average.
For a 20% tip: find 10% (move the decimal) and double it.