Why are there letters in math

Chapter 12: Algebra - Calculating with Letters


We can add up anything. Why not letters too. This chapter tells about calculating with letters.

 

Words 1

count, add up, press, express, the expression, the letter, the variable, the term, sort, alphabetically, the alphabet, summarize, summarize, separate, together, mix, like, first, the route, fly

1. Add

 
♥ + ♥ + ♥ + ♥ = ♥ =

♣ + ♣ + ♣ = ♣ =

♥ + ♥ + ♣ + ♥ + ♥ + ♣ + ♣ = ♥ + ♣ = ♥ +


 

We call such a mathematical expression with letters "Term". We call the letters "variables".

 

Exercises

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We like to sort the variables alphabetically. We like to write the number first.

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We like to leave out + (sign) and 1 (in the product).

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2. Subtract

 


 

When we add or subtract variables, we say, "We'll summarize them". We summarize the same variables and numbers separately from one another. We must not mix them up by grouping them together.

 

 

Exercises

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We like to sort the variables alphabetically. We like to write the number first.

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We like to leave out + (sign) and 1 (in the product).

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A flight route is x km long. y km you have already flown. How many km will you fly?

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3. Multiply and stand out


 

What does this calculation have to do with the picture?

café + café + perrier + perrier = 2 café + 2 perrier = 2 (café + perrier)

Note on the language

Café means in the "coffee house". The drink is called coffee. In French, the drink is written as café.

 

Lifting out

A common factor is only written once. A product is created.
2 café + 2 perrier = 2 (café + perrier)

Multiply

The multiplication is carried out. Each element is multiplied.
2 (café + perrier) = 2 café + 2 perrier

What for?

We say “variables” to c and p. If c is the price of coffee and p is the price of Perrier, then the above calculation will be the amount of money to be paid. The prices are variable (different) depending on the coffee house. The bill applies to all coffee houses. That is practical.

Words 2

the picture, do, have to do, the price, Perrier (mineral water), above, the amount, the money, the amount of money, pay, the coffee, the coffee house, variable, different, apply, practical, the value, set, use , the possibility, the person, to lift out, to emphasize, to reverse, to reverse, to settle, to divide, to split up, to describe, to shorten, to create, to conclude, simply, to simplify, everyday life, art, algebra, forbidden to wear glasses, know

If we give the variables c and p the value 1.6 and 3.2, "we put in c and p". We write the values ​​instead of c and p. We have 3 options in the above calculation.



At the 3rd term we see that each of the two people has to pay 4.8 euros. We got the third term by singling out. Highlighting is the reverse of multiplication.

Exercises

Multiply

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Lifting out

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4. Divide

When calculating with letters, divide is written as a term with a fraction line.

x could be the bill in the restaurant. It is divided between five people. The term describes how much each of the five people pays.
 

example 1


We calculate with letters even without any relation to everyday life. This art of computing is called "algebra".

 

Example 2


Simplify top and bottom first. That means: add, subtract (summarize), multiply, shorten. We'll shorten it by 7 at the end.
 

Example 3


The result cannot be simplified any further. Shortening is prohibited with + and -.
 

Extension: example 4


By singling out, we have created a “mark”. Then shortening is allowed.
 

Exercises

If x is the number of people and every 4th person wears glasses: Which term describes the number of people who wear glasses?

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Now if we know that x = 200, how many people wear glasses?

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Answer: 50 people wear glasses.

More exercises:

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5. Precedence rules

The usual priority rules apply, which can be changed using brackets. Within the brackets we want to simplify first.

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6. See you next time

Words 3

the opportunity, find, anywhere, the thing, count, the number, multiply, the question, ask, the answer, know, curious, stay

We find opportunities for arithmetic everywhere. Whether we're just counting things. Whether we're multiplying the numbers. Whether we ask questions whose answer we do not yet know. Let's stay curious!
 



Corrections: Maria Fatoba

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