Decimal fractions (decimals) Decimal fractions (decimal point, decimal places). Properties of decimals. Repeating decimals. Decimal fraction is a result of dividing of unit by ten, hundred, thousand parts etc. These fractions are very comfortable in calculations, because they are based on the same system, that calculus and record of integers are built. Due to this […]

## Operations with vulgar fractions

Operations with vulgar fractions Extension of a fraction. Cancellation of a fraction. Comparison of fractions. Reducing of fractions to a common denominator. Addition and subtraction of fractions. Multiplication of fractions. Division of fractions. Extension of a fraction. A fraction value isn’t changed, if to multiply its numerator and denominator by the same non-zero number. This […]

## Vulgar (simple) fractions

Vulgar (simple) fractions Vulgar fraction (denominator, numerator). Proper fraction. Improper fraction.Mixed number (integer and fractional parts). Converting of a mixed number into a vulgarimproper fraction and back. Reciprocal fractions. A part of a unit or some equal parts of a unit is called a vulgar (simple) fraction. A number of equal parts into which a unit has been […]

## Least common multiple

Least common multiple Common multiple of some numbers.Least common multiple (LCM). Finding LCM. Common multiple of some numbers is called a number, which is divisible by each of them. For example, numbers 9, 18 and 45 have as a common multiple 180. But 90 and 360 are also theirs common multiples. Among all common multiples […]

## Greatest common factor

Greatest common factor Common factor of some numbers.Greatest common factor (GCF). Finding GCF. Common factor of some numbers – a number, which is a factor of each of them. For example, numbers 36, 60, 42 have common factors 2 and 3 . Among all common factors there is always the greatest one, in our case […]

## Factorization. Resolution into prime factors

Factorization. Resolution into prime factors Prime factoring of composite numbers. Any composite number can be presented as a product of prime factors by the single way. For example, 48 = 2 · 2 · 2 · 2 · 3, 225 = 3 · 3 · 5 · 5, 1050 = 2 · 3 · […]

## Divisibility criteria

Divisibility criteria Divisibility of numbers by 2, 4, 8, 3, 9, 6, 5, 25, 10, 100, 1000, 11. Divisibility by 2. A number is divisible by 2, if its last digit is 0 or is divisible by 2. Numbers, which are divisible by 2 are called even numbers. Otherwise, numbers are called odd numbers. Divisibility […]

## Laws of addition and multiplication

Laws of addition and multiplication Commutative laws of addition and multiplication. Associative laws of addition and multiplication. Distributive law of multiplication over addition. Commutative law of addition: m + n = n + m . A sum isn’t changed at rearrangement of its addends. Commutative law of multiplication: m · n = n · m […]

## Order of operations. Brackets

Order of operations. Brackets If brackets are absent, the following order of operations is right: 1) raising to a power and extraction of a root (one after another); 2) multiplication and division (one after another); 3) addition and subtraction (one after another). If brackets are present, at first all operations inside brackets are executedaccording to […]

## Arithmetical operations

Arithmetical operations Addition (addends, sum). Subtraction (minuend, subtrahend, difference). Multiplication (multiplicand, multiplier, product, factors). Division (dividend, divisor, quotient, dividing integers, fraction, divisible numbers, remainder, division without remainder, division with remainder). Raising to a power (power, base of a power, index or exponent of a power, value of a power). Extraction of a root (root, […]