What should everyone know about math

Math knowledge

System of two and three

Instead of forming numbers from units, tens, hundreds and thousands, as in the system of ten, the numbers in the binary system (system of two) are formed with only two digits. The digits of the table are formed by the power of two (1, 2, 4, 8, 16, 32, 64, 128,256, 512, 1024), so it starts with ones, then two, four, eight, etc.

Roman Numbers - Spelling of numbers with letters

On many old buildings we come across numbers in the dates that do not look very similar to our Arabic numerals: the Roman numerals, named after the Romans who used these numbers in the past.

Greater and lesser - relation signs

There are numbers that are larger or smaller than others. To see which number is larger or smaller, you can use a number line to help. The small numbers are on the left, the large numbers on the right.

Round - Simplify long sequences of digits

In some situations it is unnecessary to give a very precise number, e.g. B. for long distances or large quantities. Most of the time, approximate figures are even clearer.

Scientific notation of numbers

In science, numbers are unfortunately not as handy as in most math books. There can be very large, but also very small numbers.

Divisors and divisors - definition

The divisor is a number that can be used to divide another number as an integer. The subset of a number is a set that contains all numbers by which this number can be divided as an integer, i.e. without leaving a remainder.

Divisibility rules

Rules for quickly estimating whether a number is divisible by another number.

Prime factorization - unambiguous notation of numbers as a product

The prime factorization is a way of writing a number as a unique product. In doing so, a number is broken down into products of prime numbers until it can no longer be divided. It is a unique way of spelling numbers, regardless of the order.

gcd and lcm - greatest common divisor and smallest common multiple

gcd (greatest common divisor): The greatest common divisor of two numbers is the greatest number by which both numbers can be divided. Lcm (lowest common multiple): The lowest common multiple of at least two numbers is the smallest number that can be divided by both (or more) numbers.

Set theory - set of natural numbers, whole numbers, rational numbers, set operations

This topic is barely dealt with at all or very little in school. Nevertheless, everyone interested in mathematics should know them: the quantities.

Basic arithmetic and arithmetic advantages: Written addition - Written addition

Additions (plus arithmetic) of larger numbers or a larger number of summands (summands are the numbers that are added) quickly lead to the limits of our mental arithmetic possibilities. However, there is an easy way to do this in writing.

Written Subtraction - Written Subtraction

As with adding, there is also a convenient method that allows us to subtract (subtract from) large numbers. Again, we will show you step by step how this procedure works using two examples.

Written Multiplication - Written Multiplication

To multiply large numbers that you may not be able to calculate in your head, there is a method that you can use to multiply in writing.

Written division - Written division

For dividing (dividing) large numbers, there is a method that simplifies difficult dividing.

Written arithmetic in the binary system - written addition and subtraction in the binary system

Use of the written procedure in the binary system as before in the tens system

Dot before line calculation, calculation with brackets

Calculation rules and laws for the basic arithmetic operations

Associative law (connection law) - associative laws of addition and multiplication

By cleverly connecting in arithmetic paths, we can often gain computational advantages. We use brackets to show which parts we want to calculate first. There are two associative laws, that of addition and that of multiplication.

Commutative law (exchange law) - commutative laws of addition and multiplication

There is a law for addition and multiplication that allows us to interchange summands and factors at will.

Distributive law (distribution law)

The distributive law is basically a law of multiplying parentheses. This means that you have a product (or quotient) of a number and a bracket - or two brackets. In these brackets are sums or differences. The distributive law regulates the distribution of the factor to the summands.

Fractions

Expand, shorten, order, add, subtract, multiply and divide fractions

Fractional definition

The fractions are defined as the quotient of an integer and a natural number. To avoid confusion it has to be mentioned that rational numbers are defined in the same way and therefore we state: Fractional numbers is another word for rational numbers.

Presentation of a break - Pictorial representation of breaks

We got to know the different spellings and now want to get an idea, i.e. an idea, of fractions. To illustrate breaks, cakes and pizzas are very popular. A circular area that you often split up. But any other surface is also suitable for illustrating. We just take the cake example and want to split a cake between two people. So then everyone gets half a cake.

Expand, shorten, and organize fractions

Expand, shorten and order fractions by correctly multiplying and dividing the numerator and denominator.

Fractions

Adding and subtracting, multiplying and dividing fractions

Decimal fractions - convert decimal fractions to fractions and fractions to decimal fractions

Decimal fractions are another way of representing fractions. This type of representation has very special advantages when entering into pocket calculators and computers, but the pocket calculator likes to round off and so correct fractions are advantageous for reasons of precision and also easier to use when calculating in the head or on paper. This sometimes requires a conversion from one type of representation to the other.

Percentages - Percentage as a representation of a fraction

The question is: What do percentages have to do with fractions or with fractions and decimals? The fraction alone is already in the word percent (from the Latin pro centum - "for one hundred / per hundred").

Geometry - figures, shapes, angles, figures and solids

Cube, cuboid, pyramid, cone, sphere, cylinder

to shape

Triangle (right-angled, isosceles, equilateral), rectangle (rectangle, square, parallelogram, diamond, trapezoid)