1 ESO - UNIT 09 - ALGEBRA.

1. Unit 09 April
1. ALGEBRAIC EXPRESSIONS.
We can describe everyday situations using Algebra. In Algebra, you use letters
to represent unknown numbers. An Algebraic Expression is an expression built up
from integer constants, variables, and the algebraic operations.
2𝑛𝑛 + 3
This expression means the double of a number plus three
An Algebraic Expression has numbers and letters linked by operations. The
letters are called Variables. Every addend is called Term.
You can simplify an algebraic expression by collecting Like Terms. Like Terms
have exactly the same letters.
2𝑛𝑛 + 3𝑛𝑛 = 5𝑛𝑛
You can find the value of an algebraic expression when you know the value of
the letters used.
𝐼𝐼𝐼𝐼 𝑛𝑛 = 2 ⇒ 5𝑛𝑛 = 5 ∙ 2 = 10
Evaluating an Algebraic Expression is the same as calculating its number value
at a given value of the variables.
MATH VOCABULARY: Algebra, Algebraic Expression, Variable, Term, Like Terms,
Constant, Coefficient, Evaluating Algebraic Expression.
Axel Cotón Gutiérrez Mathematics 1º ESO 9.1

2. Unit 09 April
2. MONOMIALS.
A Monomial is an Algebraic Expression containing one Term which may be a
number, a Variable or a product of numbers and variables, with no negative or
fractional exponents. (Mono implies one and the ending nomial is Greek for part).
5𝑥𝑥; −2𝑦𝑦; 450𝑥𝑥2
𝑧𝑧 are monomials
The number is called Coefficient and the variables are called Literal Part. If the
literal part of a monomial has only one letter, then the Degree is the exponent of the
letter. If the literal part of a monomial has more than one letter, then the degree is the
addition of the exponents of the letters.
The degree of −5𝑥𝑥3
is 3
The degree of 2𝑥𝑥2
𝑦𝑦3
𝑧𝑧 is 2 + 3 + 1 = 6
2.1. ADDITION AND SUBTRACTION OF MONOMIALS.
You can add monomials only if they have the same Literal Part (they are also
called Like Terms). In this case, you add the coefficients and leave the same literal part.
3𝑥𝑥 + 5𝑥𝑥 = 8𝑥𝑥
3𝑥𝑥 − 2𝑥𝑥2
You cannot add the terms because they have different literal part.
2.2. MULTIPLICATION AND DIVISION OF MONOMIALS.
If you want to multiply two or more monomials, you just have to multiply the
coefficients, and add the exponents of the equal letters.
Axel Cotón Gutiérrez Mathematics 1º ESO 9.2

3. Unit 09 April
2𝑥𝑥7
∙ 3𝑥𝑥3
= (2 ∙ 3) ∙ 𝑥𝑥7+3
= 6𝑥𝑥10
(−2𝑥𝑥𝑦𝑦2
𝑧𝑧) ∙ (5𝑥𝑥2
𝑧𝑧3) = �(−2) ∙ 5� ∙ (𝑥𝑥1+2) ∙ (𝑦𝑦2+0) ∙ (𝑧𝑧1+3) = −10𝑥𝑥3
𝑦𝑦3
𝑧𝑧4
If you want to divide a monomial by a monomial of the same or lower degree,
you just have to divide the coefficients, and subtract the exponents of the equal
letters.
10𝑥𝑥5
÷ 2𝑥𝑥2
= (10 ÷ 2) ∙ (𝑥𝑥5−2) = 5𝑥𝑥3
(12𝑎𝑎2
𝑏𝑏) ÷ (3𝑎𝑎) = (12 ÷ 3) ∙ (𝑎𝑎2−1) ∙ (𝑏𝑏1−0) = 4𝑎𝑎𝑎𝑎
MATH VOCABULARY: Monomial.
3. IDENTITIES, FORMULAE AND EQUATIONS.
An Identity is true for all values of x.
3𝑥𝑥 + 5𝑥𝑥 = 8𝑥𝑥
An Equation is only true for a limited number of values of x.
2𝑥𝑥 − 1 = 1
A Formula describes the relationship between two or more variables.
𝐴𝐴 = 𝑏𝑏 ∙ ℎ
MATH VOCABULARY: Identity, Equation, Formulae.
Axel Cotón Gutiérrez Mathematics 1º ESO 9.3

4. Unit 09 April
4. FIRST-DEGREE EQUATIONS.
4.1. PARTS OF AN EQUATION.
An Equation is a statement using algebra that contains an unknown quantity
and an equals sign. The Solution of an equation is the set of values which, when
substituted for unknowns, make the equation a true statement. An Equation has
different Elements:
• Variables: The unknown quantities
• Member: The two expressions on either side of an equation.
• Term: Any of the addends of an equation.
• Degree: For a term with one variable, the degree is the variable's exponent. With
more than one variable, the degree is the sum of the exponents of the variables.
4.2. FIRST-DEGREE EQUATIONS.
A First-Degree Equation is called a Linear Equation. The highest exponent of a
linear equation is 1. The standard form for a linear equation is:
𝒂𝒂, 𝒃𝒃, 𝒄𝒄 ∈ ℤ 𝒂𝒂𝒂𝒂𝒂𝒂 𝒂𝒂 ≠ 𝟎𝟎
Axel Cotón Gutiérrez Mathematics 1º ESO 9.4

5. Unit 09 April
3𝑥𝑥 + 2 = −10.
The solution of this equation is 𝑥𝑥 = −4
In an equation the equals sign shows that the sides balance. To solve an
equation you must always keep the balance.
MATH VOCABULARY: First-Degree Equation, Linear Equation.
Axel Cotón Gutiérrez Mathematics 1º ESO 9.5

6. Unit 09 April
5. SOLVING PROBLEMS USING EQUATIONS.
Word Problems are a series of expressions that fits into an equation.
If you add 7 to a number you obtain the triple than if you subtract 5. Which is the
number?
The number ⤇ 𝑥𝑥
The number plus 7 ⤇ 𝑥𝑥 + 7
The number minus 5 ⤇ 𝑥𝑥 − 5
𝑥𝑥 + 7 = 3(𝑥𝑥 − 5)
𝑥𝑥 + 7 = 3𝑥𝑥 − 15
𝑥𝑥 − 3𝑥𝑥 = −15 − 7
−2𝑥𝑥 = −22
𝑥𝑥 =
−22
−2
= 11
Checking:
11 + 7 = 18 𝑎𝑎𝑛𝑛𝑛𝑛 11 − 5 = 6
18 = 3 ∙ 6
Axel Cotón Gutiérrez Mathematics 1º ESO 9.6