TRANSLATING KEY WORDS AND PHRASES INTO ALGEBRAIC EXPRESSIONS The table below lists some key words and phrases that are used to describe common mathematical operations. To write algebraic expressions and equations, assign a variable to represent the unknown number. In the table below, the letter “x” is used to represent the unknown. In translation problems, the words sum, total, difference, product and quotient imply at least two parts – use parentheses when a sum or difference is multiplied. For example, the phrase "the sum of three times a number and five" translates to "3x + 5," while the phrase "three times the sum of a number and five" translates to "3(x + 5)." OPERATION Addition ( + ) KEY WORD/PHRASE plus more than the sum of the total of increased by added to Subtraction ( − )

EXAMPLE A number plus three Ten more than a number The sum of a number and five The total of six and some number A number increased by two Eleven added to a number A number minus seven Four less than a number The difference of a number and three Nine less a number A number decreased by twelve Six subtracted from a number Eight times a number The product of fourteen and a number Twice a number; double a number A number multiplied by negative six Three fourths of a number The quotient of a number and seven Ten divided by a number The ratio of a number to fifteen The square of a number; a number squared The cube of a number; a number cubed Seven less than a number equals ten. Three times a number is negative six. Eight is the same as twice a number. Twelve added to a number yields five. Nine less a number amounts to twenty.

TRANSLATION x+3 x + 10 x+5 6+x x+2 x + 11
X–7 X–4 X–3

minus less than the difference of less decreased by subtracted from

9–X
X – 12 X–6

Multiplication ( x )

times the product of twice; double multiplied by of

...TRANSLATE WORD SENTENCES INTO ALGEBRAICEXPRESSIONS
The following table lists the most common phrases and their translation.
|Operation |Words |Example of Phrase |Algebraic Sign |Algebraic |
| | | | |Translation |
|Addition |sum |the sum of a number and 2 | + |x + 2 |
| |plus |two plus a number | | |
| |added |two added to a number | | |
| |more than |two more than a number | | |
| |increased by |a number increased by 2 | | |
|Subtraction |difference |the difference of a number and two |- |x - 2 |
| |minus |a number...

...In mathematics, an algebraicexpression is an expression built up from constants, variables, and a finite number of algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).[1] For example, is an algebraicexpression. Since taking the square root is the same as raising to the power ,
is also an algebraicexpression.
A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetics operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions). In other words, a rational expression is an expression which may be constructed from the variables and the constants by using only the four operations of the arithmetic. Thus, is a rational expression, whereas is not.
A rational equation is an equation in which two rational fractions (or rational expressions) of the form are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.
Algebra has its own...

...
Like and unlike algebraic terms
Like algebraic terms are defined as those terms which are represented by the same algebraic symbol, regardless of the sign or the magnitude of their coefficients.
Thus 5x, –3x, [pic] and [pic] are like algebraic terms since they are all represented by the same symbol x.
Similarly 3a2 , –2a2, 0.4a2 and [pic]a2 are like terms.
Unlike algebraic terms are terms that are represented by different algebraic symbols.
Thus 7b, 3b2 and –2b3 are all unlike terms even though they are powers of the same variable, b.
Similarly, [pic], [pic]and [pic], read as “y one”, “y two” and “y three” respectively, are unlike algebraic terms and are interpreted as the “first y”, the “second y” and the “third y” .
AlgebraicExpressions
When we combine numbers and variables with the ordinary operations of arithmetic (in some meaningful way), the result is called an algebraicexpression. Addition/subtraction signs separate algebraicexpressions into terms.
For example,
(1) 2 + 3x – 4y + 5z, (2) 7a2 b3 + 5, (3) (x – y)(y – z)(z – x), (4) [pic].
The expressions above have no specific value unless we assign values to the variables
a, b, x, y, and z. The values of these expressions may vary depending on the values assigned to...

...Subtraction and Addition of AlgebraicExpressions
Math 11
Objectives
The student should be able to:
Determine the degree of a polynomial
Identify the fundamental operations of polynomials
Definition of Terms
Algebraicexpression is an expression involving constants and or variable, with all or some of the algebraic operations of addition, subtraction, division and multiplication
Definition of Terms
Components of an
AlgebraicExpression
Constant term: fancy name for a number
Variable term: terms with letters
Example: 3xy – 4z + 17
Variable expression with 3 terms:
3xy, -4z, 17
2 variable terms and 1 constant term
Variable Terms
Consist of two parts
The variable(letter) part
The number part
Example:
2xy has a coefficient of 2
-6j has a coefficient of –6
W has a coefficient of 1
Definition of Terms
Monomial an algebraicexpression containing only one term
ex. 4xy4
Binomial an algebraicexpression containing two terms
ex. 4a + 3b
Trinomial an algebraicexpression containing three terms
ex. 2a + 5b + 3c
Definition of Terms
Polynomial an algebraicexpression containing two or more terms
An algebraicexpression in which each term is a constant, or a...

...A L G E B R A spells algebra. Duh. ffffffffffffffffffhjhdfjj
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During the last summer vacation, I received an invitation from my friend to spend the vacation at Allahabad. The idea of journey is filled my heart with pleasure.
Preparation before the start:
I at once started preparation for the journey. At last the day came when I was to leave for Allahabad. I...

...Rational AlgebraicExpressions
4. Rational AlgebraicExpressions
Note You need to understand how to multiply algebraicexpressions using the distributive law before starting work on this tutorial. If you feel you need to review this, go back to 3. Multiplying and Factoring AlgebraicExpressions.
Q What is a Rational Expression?
RationalExpression
A rational expression is an algebraicexpression of the form P/Q, where P and Q are simpler expressions (usually polynomials), and the denominator Q is not zero.
A rational number is any number that can be written in the form a/b, where a and b are integers and b ≠ 0. it is necessary to exclude 0 because the fraction represents a ÷ b, and division by zero is undefined.
A rational expression is an expression that can be written in the form P/Q where P and Q are polynomials and the value of Q is not zero.
Some examples of rational expressions:
-5/3; (x^2 + 1)/2; 7/(y -1); (ab)/c; [(a^2)(b]/c^2; (z^2 + 3z + 2)/ (z + 1) ect.
Like a rational number, a rational expression represents a division, and so the denominator cannot be 0. A rational expression is undefined for any value of the variable that makes the denominator equal to 0. So we say that...

...Keywords
Chapter 1
1. Absolute price level : A measure of the overall level of prices in the economy.
2. Barriers to entry: Structural, legal, or regulatory characteristics of a firm and its market that keep other firms from easily producing the same or similar products at the same cost.
3. Fiscal policy: Changes in taxing and spending by the executive and legislative branches of a country’s national government that can be used to either stimulate or restrain the economy.
4. Gross domestic product (GDP): The comprehensive measure of the total market value of all currently produced final goods and services within a country in a given period of time by domestic and foreign supplied resources.
5. Imperfect competition: Market structures of monopolistic competition, oligopoly, and monopoly, in which firms have some degree of market power.
6. Inputs：The factors of production, such as land, labor, capital, raw materials, and entrepreneurship, that are used to produce the outputs, or final goods and services, that are bought and sold in a market economy.
7. Macroeconomics：The branch of economics that focuses on the overall level of economic activity, changes in the price level, and the amount of unemployment by analyzing group or aggregate behavior in different sectors of the economy.
8. Markets：The institutions and mechanisms used for the buying and selling of goods and services. The four major types of markets in microeconomic analysis are...

...encloses an area of 121 cm2. If the same wire is bent in the form of a circle, find the area enclosed by it.
9. The area of a circular tin plate is 38.5 m2. Find its circumference.
10. The diameter of a circular park is 84 m. A 3.5 m vide road on the outside around it. Find the cost of constructing road @ Rs. 200 per m2.
*******
RYAN INTERNATIONAL SCHOOL - ROHINI
CLASS: VIII
WORK SHEET
ALZEBRAIC EXPRESSIONS
1. (2x + 5) (2x – 5) = ?
(a). (4x2 +25) (b). (4x2 – 25) (c). (4x2 -10x = 25) (d). (4x2 + 10x – 25)
2. (a -1) (a +1) (a2 +1) = ?
(a). (a4 -2a2 -1) (b) (a4 – a2-1) (c). (a4 -1) (d). (a4 +1)
3. ( x + 1/x) = 5, then (x2+ 1/x2) = ?
(a(. .25 (b). 27 (c) 23 (d) 251/25)
4. If (a –b) =7 and ab = 9, then (a2 +b2= ?
5. If x = 10, then value of ( 4x2 + 20x + 25) = ?
(a). 256 (b) 425 (c) 625 (d) 575
6. Add: 8x2 -5xy +3y2, 2xy -6y2 + 3x2 and Y2 + xy – 6x2
7. Multiply: (i) 5x2 -6x +9) by (2x – 3) (ii) (2x2 -5x +4 ) by (x2 +7x - 8)
8. Find the value of the expression (81x2 + 16y2 -72xy), when x= 2/3 and y = 3/4...

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