Numerical expressions - order of operations and solved examples

Numerical expressions are essential for knowledge of maths, and very important in its use in every day. To help you study maths, here you will learn what are numerical expressions and how to calculate numerical expressions. 

Numerical expressions

A numerical expression is a way of expressing reasoning in a problem and another way to represent a number. Any numerical expression represents a value. But you perceive better checking the following example: 

John went to the supermarket with 10 dollars and bought two cans of mushrooms and a bag of flour. Knowing each can of mushrooms cost $1.30 and the package flour $1.10, indicate: 

a) how much money was spent. 

To solve this problem, you must use the numerical expression: 2 x 1.30 + 1.10 

2 x 1.30 + 1.10 expresses the amount he spent, which is equal to $3.70. 

b) how much money is left. 

To solve this problem, you must use the numerical expression: 10 - (2 x 1.30 + 1.10) 

10 - (2 x 1.30 + 1.10) expresses the value that is left, which is equal to $6.30. 

How to calculate numerical expressions 

To learn how to calculate numerical expressions, is critical to realize that exists a series of operations, and so, there must be rules to implement them. This rules are called order of operations. So, to calculate numerical expressions, you have to know the order of operations of numerical expressions. Below, you can find an example with the rules explained to you understand more easily. 

• Order of operations

In a numerical expression, the operations are not made simply by the order in which they appear. Each type of operation has a priority, which indicates which operations must be done in the first place. Then you can check the order of operations to calculate numerical expressions. 

1st Priority - Firstly, make all calculations within parentheses (these calculations must follow the rules described below). 

2nd Priority - For operations, we must first make the exponents or roots. 

3rd Priority – Calculate the multiplications and divisions in the order they appear. 

4th Priority - Finally, calculate the additions and subtractions in the order they appear. 

• Solved examples of numerical expressions 

Let's start with a simple numerical expression: 

    23-4 x 5 =    --- 3rd P - Make first the multiplication 

= 23-20 =         --- 4th P – Make the subtraction 

= 3 

Now a solved example a little more complicated:

Types of trapezoids

The trapezoid is a quadrilateral polygon, which has two opposite parallel sides and two non-parallel opposite sides. The parallel sides are the biggest and smallest bases. There are three types of trapezoids: rectangle, isosceles and scalene. Below you can learn more about each of these types of trapezoids.

• Rectangle trapezoid

 

The rectangle trapezoid is a trapezoid in which a side is perpendicular to both bases. 

• Isosceles trapezoid

The isosceles trapezoid is a trapezoid in which the opposite two parallel sides are not equal. 

• Scalene trapezoid

The scalene trapezoid is a trapezoid in which all sides have different measures. 

Tangram Alphabet: Building Letters With Tangrams

Tangram is an ancient chinese game, that consist in create various figures with 7 geometric pieces. Today, despite being very old, this is a very popular game, serving for fun, but also, to develop the skills of spatial vision, logic, geometry, and creativity. This is a very helpfull game to study maths.

Below you can learn how to make all the letters of the alphabet with Tangrams. But before, it is essential having a tangram. If you do not have one and dont want to buy, dont worry. With just a sheet of paper and a scissor, you can build a tangram puzzle. Click HERE to learn how to build a tangram puzzle. 

After you have built your tangram puzzle, then you can try to make all the letters in the alphabet tangram. 

Tangram alphabet: building letters with tangrams 

A B C D E F G H 

I J K L M N 

O P Q R S 

T U V W 

Y X 

Z 

Below, you can find the resolution for each letter of the alphabet in Tangram.

Tangram Alphabet: Building Letters With Tangrams - SOLUTIONS

Play online chess with a friend

One of the best math games ever is chess. With simple rules, but needing extensive reasoning ability, this is the game to have fun and evolve your maths thinking. In some countries of Eastern Europe, chess comes even part of the school curriculum, helping children develop reasoning. Here you cand play online chess with a friend.

Chess is seen by many as a big deal, but in reality it is a very interesting and fun game. Take a chance on this fantastic game and develop your reasoning. 

Before you start playing online chess with a friend, it is important to know the basic rules of chess. Learn about the basic rules of this game in our article "Basic Rules of Chess". 

If you already know the basic rules, start now to play online chess with a friend.

Xadrez online criado por JogueXadrez.com

Basic rules of chess

Foto de Jeff Dahl

Chess is a game with two players, which is played on a square board with 8 houses on each side. The board has just 64 houses, 32 white and 32 black. Each player starts with 16 pieces (one king, one queen, two bishops, two knights, two towers, and eight pawns). The set of pieces of each player has a different color, so there is a set of black pieces and a set of white pieces. The ultimate goal of this game is to capture the opponent's king, making checkmate.

The initial position in chess is as follows:

First row, from right to left: Tower, Knight, Bishop, King, Queen, Bishop, Knight, Tower. The White King is in black square, and the black king is in the White House. The second line consists in eight pawns.

To start the game, the player with the white pieces makes the first move. Players move their pieces alternately. Each piece has a different movement, and every player has to respect these movements. When you capture a opposing piece (non-mandatory) , that piece is removed from the board. When you capture a piece, your piece is placed in the place of the captured piece. When you put the king in a checkmate or a stalemate is reached, the game ends. Then we explain the movement of each piece.

Basic rules of chess - movements

Before we cover the movements of each piece, it is crucial you know each one of the chess pieces.

King, Queen, Bishop, Rook, Knight and Pawn

• King

The King may move a house vertically, horizontally or diagonally. The King can never be put in the check position. When you can not avoid it, you lose.

• Queen

The queen can move horizontally, vertically or diagonally. The number of homes depends on the pieces that are on the board, since it can not pass through them.

• Bishop

The bishop can only move diagonally. The number of house depends on the pieces that are on the board, since it can not pass through them.

• Knight

The Knight is the only piece that can go over the other parts. The movement is in L, walked a house horizontally or vertically, and another diagonally. In the following image you can see the possible movements of the knight.

• Tower

The tower moves horizontally and vertically. The number of houses depends on the pieces that are on the board, since it can not pass through them.

• Pawn

The pawn moves usually a house upright, and only forward. However, there are situations where the movement of the pawns is different. For example, to capture a piece, you can just do it walking from a house diagonally across the board. Another different movement is when you are at the starting house. In its first movement, the pawn can move two squares forward.

Basic rules of chess - special moves

• Castling

The castling is a movement which seeks to defend the King In this movement, the king moves two squares to the side, and the tower moves as well, passing over the King and getting to his side. You only can make this move if the houses between the King and the Tower are empty, and if the king is not in check. Additionally, the King and the Tower which is used for castling may not have yet been moved. This movement can be done to the right or left side, existing small castling and big castling.

• Promote pawn

If a pawn reach the last house, its promoted, being replaced by a piece from your choosen, except for the King. 

• Take the passage

This move only works when a pawn began with an advance of two houses, and simultaneously, the opposing pawn is in position to attack the house where the other passed pawn. In this case, the opponent's pawn can capture the other, moving to a halfway house. This movement can only occur on the next play.

Calculate the area of ​​a triangle

Area is the surface that a given figure occupies. Before we show you how to calculate the area of ​​a triangle, observe the following situation: 

Through this practice activity, one comes to the conclusion that if we divide a parallelogram by its diagonal, we get two equal triangles. Thus, we can say that the area of each triangle will be equal to half the area of the parallelogram. If the area of the parallelogram is equal to the product of its base by its height, then the area of a triangle equals half the product of its base by its height. 

To calculate the area of ​​a triangle simply apply the following formula: