TRANSLATE WORD SENTENCES INTO ALGEBRAIC EXPRESSIONS
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 minus 2 | | | | |subtracted from |two subtracted from a number | | | | |less than |two less than a number | | | | |decreased by |a number decreased by two | | | | |reduced by |a number reduced by two...

...TRANSLATING KEY WORDS AND PHRASES INTO ALGEBRAICEXPRESSIONS
The table below lists some key words and phrases that are used to describe common mathematical operations. To write algebraicexpressions 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, thewords 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...

...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...

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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...

...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...

...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...

...Common Phrases and Expressions in English
Word/Expression: to wolf something down
Quick translation: to eat something quickly
Example: "I wolfed down that sandwich so quickly."
My interpretation: Wolves are known for eating their food quickly, for fear that another wolf will get to it before them. So to "wolf something down" is to eat as quickly as a wolf does.
Word/Expression: gotta
Quick translation: to have to/to need to
Example: "I gotta leave now."
Word/Expression: to go (expression used where food is sold)
Quick translation: to carry out/to take out with you
Example: a waiter or salesperson may ask "Would you like (your food) to go?"
Word/Expression: sick (when used to describe a person's mind or an event)
Quick translation: strange or perverted
Example: "That person is sick!" or "What he did to her is sick!"
Word/Expression: What's up?
Quick translation: a very casual way to say "Hi" or "How are you?" or "What is happening here?"
Word/Expression: handy
Quick translation: very useful, very industrious, or able to fix things themself
Example: "Her husband is very handy around the house."
Word/Expression: to catch a taxi / cab
to hail a cab/taxi
Quick translation: to get a taxi / cab
Example: "Let's...

...
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...

...Foreign Words and Phrases.
Irina Vardanyan
Foreign words and phrases shouldn't become a bête noire,
but, ceteris paribus, English sentences should be in English…
(Jack Lynch 2008)
Throughout its history, English has been shaped and enriched by words and phrases of French, Scandinavian, Italian, Latin, Greek and German origin. When cultures come into contact with one other, borrowing takes place primarily in the realm of lexical terms (Anderson 1973). As A. I. Smirnitsky points out, a foreign word is a shapeless piece of material, which gains its shape only by means and in the system of the new language (Смирницкий 1954). Many words of foreign origin have been in the English language for so long that they have been freely integrated and can no longer be distinguished from English words and may not trigger a sense of “foreignisms”. However, there are cases, when the word is not assimilated and retains its foreign language spelling, pronunciation as well as foreign language connotation. Such cases are perceived as “organic inclusions” (Смирницкий 1954).
Depending on the degree to which the originally “alien” word has been adapted to its new linguistic surroundings, linguists distinguish between foreign words and loanwords. However, the borderline between...

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