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Arithmetic Formulas & Calculators

Understand arithmetic formulas with explanations, examples and interactive tools.

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Addition

\(a+b\)

Combine two quantities.

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Subtraction

\(a-b\)

Find the difference between two quantities.

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Multiplication

a\times b

Repeated addition of equal groups.

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Division

a\div b

Share a quantity into equal groups; divisor must not be zero.

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Place Value

d\times 10^n

Value of a digit depends on its position.

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Money Conversion

\text{paise}=100\times\text{rupees}

One rupee equals one hundred paise.

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Total Cost

\text{price}\times\text{quantity}

Multiply price per item by number of items.

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Remainder Relation

\(a=bq+r\)

Dividend equals divisor times quotient plus remainder; 0 ≤ r < |b|.

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Even Number

\(n=2k\)

An integer is even when divisible by 2.

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Odd Number

\(n=2k+1\)

An integer is odd when it is one more than an even integer.

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Fraction of a Quantity

\frac{a}{b}\times N

Find a fractional part of a whole number.

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Fraction Addition

\frac ab+\frac cd=\frac{ad+bc}{bd}

Add two fractions using a common denominator.

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Fraction Multiplication

\frac ab\times\frac cd=\frac{ac}{bd}

Multiply the numerators and denominators.

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Average (Mean)

\bar x=\frac{\sum x_i}{n}

Add values and divide by number of values.

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Percentage

p=\frac{\text{part}}{\text{whole}}\times100

Express part of a whole out of one hundred.

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Percent of a Number

x\times\frac{p}{100}

Calculate a given percentage of a number.

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Ratio Simplification

a:b=\frac{a}{g}:\frac{b}{g}

Divide both terms by their greatest common divisor.

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HCF of Two Integers

\operatorname{HCF}(a,b)

Greatest positive integer dividing both integers.

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LCM of Two Integers

\operatorname{LCM}(a,b)=\frac{|ab|}{\operatorname{HCF}(a,b)}

Smallest nonnegative common multiple; both nonzero for positive LCM.

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Simple Interest

SI=\frac{PRT}{100}

Interest on principal P at annual rate R% for T years.

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Profit

\text{Profit}=SP-CP

Selling price minus cost price.

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Profit Percentage

\frac{SP-CP}{CP}\times100

Profit relative to cost price; CP must be positive.

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Discount

D=\frac{MP\times d}{100}

Discount on marked price at rate d%.

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Speed

v=\frac{d}{t}

Speed equals distance divided by elapsed time.

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Distance

\(d=vt\)

Distance at constant speed.

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Time

t=\frac{d}{v}

Travel time at constant nonzero speed.

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Compound Amount

A=P(1+\frac{r}{100})^t

Amount with annual compounding.

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