Ratio and proportion. Proportionality Ratio. Proportion ( border and middle terms ).The main property of a proportion. Proportional values. Factor of a proportionality. Ratio is a quotient of dividing one number by another. Proportion – an equality of two ratios. For instance: 12 : 20 = 3 : 5; a : b = c : d . Border terms of … [Read more...]

## Percents

Percents Percent. Three main problems by percents. Percent is a hundredth part of unit. A record 1% means 0.01. There are three main problems by percents: Problem 1. Find an indicated percent of a given number. The given number is multiplied by the indicated number of percents; then a product is divided by 100. E x a m p l e . A … [Read more...]

## Converting a decimal to a vulgar fraction and back

Converting a decimal to a vulgar fraction and back To convert a decimal to a vulgar fraction it is necessary: a number after a decimal point to make as the numerator, and the n-th power of 10 ( here n – a quantity of decimal places ) - as the denominator. A non-zero integer part of a decimal is saved the same in a vulgar fraction; a zero integer part is omitted. For … [Read more...]

## Operations with decimal fractions

Operations with decimal fractions Addition and subtraction of decimals. Multiplication of decimals.Division of decimals. Division of decimal fraction by integer. Division of decimal fraction by another one. Addition and subtraction of decimals. These operations are executed as well as an addition and a subtraction of whole numbers. It is only necessary to write the … [Read more...]

## Decimal fractions (decimals)

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 … [Read more...]

## 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 … [Read more...]

## 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 … [Read more...]

## 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 there is always the least one, in our case … [Read more...]

## 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 this is 6. This number is called a greatest common … [Read more...]

## 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 · 5 · 5 · 7. For small numbers this operation is easy. For large numbers it is possible to use the following way. … [Read more...]