# Hatsudy

## Multiply and Divide Polynomials, Distributive Property, and Substitutions

A mathematical equation that uses the alphabet is an algebraic expression. In junior high school and high school math, we need to understand how to use algebraic expressions because they are almost always used in math. An equation that consists of several algebraic expressions is called polynomials. In polynomial calculations, multiplication and division are frequently […]

## Algebraic Expressions of Monomials and Polynomials: Addition and Subtraction

In mathematics, we use letters to perform calculations. This is called an algebraic expression. Before learning the algebraic expression, calculations are done using only numbers. However, after learning algebraic expressions, math is mainly done by using the alphabet. Algebraic expressions have rules. Therefore, you have to learn how to use algebraic expressions. There are also […]

## Commutative Property and Associative Property: Addition and Multiplication in Math

When you study mathematics, you may be taught about the commutative property (or commutative law) and the associative property (or associative law). The commutative property and the associative property are taught in elementary or junior high school. The commutative property and the associative property are valid for addition and multiplication. The commutative property and the […]

## Four Arithmetic Operations of Positive and Negative Numbers: Priority of Math Calculations

After learning addition, subtraction, multiplication, and division for positive and negative numbers, students need to be able to calculate expressions that mix each of them. Addition, subtraction, multiplication, and division are collectively called the four rules of arithmetic. In mathematics, we study the four rules of arithmetic (four arithmetic operations). After learning about positive and […]

## Positive and Negative Numbers: Multiplication, Division and Power

When learning negative numbers, many people get confused. This is because when you multiply or divide different signs, the signs change. In addition, when you multiply negative by negative, the sign becomes positive. Why does this happen? Few people can explain this reason. However, in order to understand mathematics, we need to solve the question […]

## Positive and Negative Numbers: Addition and Subtraction / Absolute Value

When you learn math, you have to understand negative numbers. Unlike when you were learning only positive integers, learning the concept of zero and addition and subtraction will allow you to perform complex calculations. It may seem strange to you that there are numbers less than zero. However, we use negative numbers in many aspects […]

## Aromatic Heterocyclic Compounds: Reactivity and Orientation

There are many types of compounds that have aromatic properties. All compounds are aromatic if they have a benzene ring in the molecule. However, there are aromatic compounds that are different from benzene rings. These are heterocyclic compounds. Aromatic heterocyclic compounds show aromaticity but have different properties from benzene rings. What should we pay attention […]

## Diels-Alder Reaction of Pericyclic Reactions: Dienes and Dienophiles

When synthesizing a compound with a six-membered ring, there is one synthetic reaction to consider first; the pericyclic reaction. Among the pericyclic reactions, the most famous is the Diels-Alder reaction. In organic chemical reactions, Lewis acids and Lewis bases are usually involved in the reaction. In the pericyclic reaction, however, acids and bases are not […]