# Why are there letters in math

## Chapter 12: Algebra - 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

♥ + ♥ + ♥ + ♥ = ♥ = ♥

♣ + ♣ + ♣ = ♣ = ♣

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

### Exercises

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

### solution

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

### solution

### 2. Subtract

### Exercises

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

### solution

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

### solution

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

#### 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

#### 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?

### solution

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

### solution

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.

### exercise

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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

Found a mistake? Please send an email to [email protected] Many Thanks!

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