Thursday, 28 February 2013

Algebra ... Nomenclature

(I) Algebraic Expressions vs Equations
The following are expressions

  • 3x
  • 5 - 2y
  • p + 2q - 45
  • mn
The following are equations:
  • 2x = 4
  • x + 8 = 20
  • x² = 36
  • 2x + y = 4
Can you tell the difference between an expression and an equation?

(II) Coefficients, Variables and Constants
In the following algebraic expressions:

(a) 6x
  • x is a variable
  • 6 is the coefficient of x
  • There is no constant
(b) 2y + 5
  • y is a variable
  • 2 is the coefficient of y
  • 5 is the constant
(c) 3m + 7n + 9
  • m and n are variables
  • 3 and 7 are coefficients of m and n respectively
  • 9 is the constant
(d) p + 2q - 45
  • p and q are variables
  • 1 and 2 are coefficients of p and q respectively
  • -45 is the constant
(e) 5a - 3b + 1
  • a and b are variables
  • 5 and -3 are coefficients of a and b respectively
  • 1 is the constant
(f) x - y
  • x and y are variables
  • 1 and -1 are coefficients of x and y respectively
  • There is no constant
When given an expression, are you able to pick out the variable(s), coefficient(s) and constant terms?


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27 comments:

  1. You have to solve an equation, but you expand, etc, etc... for an expressions.
    Yes I can.

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  2. For equations, you have to solve it but for expressions, you either expand, simplify, etc.
    Yes.

    ReplyDelete
  3. From the post I understand that you may or may not be able to solve expressions, while you can solve an equation. Constants are numbers that will always remain the same. Variables are letters that can represent any number. While coefficient numbers are a 'mix' of constants and variables.

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  4. When a alphabet is by itself , it is a variable , when it is with a number , the number and the alphabet become coefficent. finally , a number by itself is a constant.

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  5. Can you tell the difference between an expression and an equation?

    An equation has a end result with and equal sign while expressions have no equal sign


    When given an expression, are you able to pick out the variable(s), coefficient(s) and constant terms?

    Yes. The letters are the variables and when we are faced with terms like x-y, we take it as 1x-1y, thus we can get the coefficients and variables.

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  6. An expression is just a number or a variable; or could be both combined. An expression is a problem with an '=' sign.
    Yes

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  7. An expression means that they are just numbers combined by +, -, division or x. An equation comes from the word 'equal', thus has the = sign in it.
    Variables are numbers that change. Coefficients are numbers in front of the variable that will change too. Constant terms are terms/ numbers that will not change, remain constant.

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  8. i learnt the difference between variables, constants and i know together they're coefficient. expressions are number sentences containing variables constants and or coefficients but without the answer while equations are expressions with the answer to the number sentence.

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  9. You have to solve equations but you either expand or simplify expressions.

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  10. Expressions are workings without answers
    Equations are workings with answers and you have to fund what the variable is.

    Variable is an unknown that you have to find while solving an equation.
    Coefficients are a multiple of the variable.
    Constants are numbers by itself.

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  11. An expression cannot be solved by itself as well there are no clue or anything else. Equations however can be solved as there are clues and other numbers to work with.
    Variables can represent any number and can be changed. Constants are.....constant. Coefficient numbers are a combination of both.

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  12. In expressions, there are variables that we do not know so we cannot solve but can only simplify it.
    I equations we know the variables so we can solve the question.
    In algebra, the letters alone are variables, the numbers alone are constants but together, the numbers are the coefficients of the letters

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  13. 1. Yes, I can.
    -An expression does not have a definite solution.
    -An expression is a set of terms with mathematical operations combining them.
    -An equation consists of two expressions with an equals sign between them.
    -An expression is a collection of terms and does not have an = sign
    2. Yes, I can.
    -The variables are the letters or numbers that change.
    -The coefficients are a constant quantity placed before and multiplying the variable in an algebraic expression.
    -A number that never changes.

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  14. An equation is when you find an answer to a problem and an expression is when you have to expand,simplify.A variable can change for example x can be 7 today,2 tomorrow.A constant is like 7. 7 will always be 7.

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  15. An equation is a result with an equal sign but an expression is a result with no equal sign

    Yes. The letters are the variables and wehen we are faced with terms like x+y, It is the same as 1x+1y so ii is possible to get the get the coeefficient and variables.

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  16. (I) The difference between equation and expressions are that equations can be solved to give a final number, while an expression is just there, although it can be simplified.
    (II)A variable is something that you do not know, that can be changed depending on the circumstances. A constant is something that never changes, its value stays the same. A coefficient is something that cannot be changed yet can , depending on the variable it is with.

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  17. Can you tell the difference between an expression and an equation?
    An expression is a string of numbers put together in a number sentence which does not need to be solved/simplified. An equation, however, is a number sentence that is solved.

    When given an expression, are you able to pick out the variable(s), coefficient(s) and constant terms?
    Yes. The variables are the letters that represent numbers (e.g. 'x'/'y')
    The coefficients are the numbers which are supposed to be multiplied by the variable. (e.g. 5x -> 5 is the coefficient)
    The constants are basically numbers that are 'on its own' as in they do not have a variable 'next to them'. (e.g 1,2,3,4,etc.)

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  18. The diference between an expression and an equation:
    An expression have no equal signs, but equations has equal signs, and can be solved, getting a result.

    Picking out variables, coefficients and constants:
    Yes. some examples of variables are x , y, z etc... Examples of coefficients are 6x, 6 is the coefficient of x. An example of a constant is 4.

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  19. An expression is something you can't solve but you can simplify or expand.
    An equation is something you can solve and there is an answer.
    Yes.

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  20. Equations have to be solved while expressions are to be expanded, simplified, etc.
    Variables have no fixed value while constants have a fixed value and will not change. Coefficients are constants merged with variables.

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  21. We can only simplify an expression but can solve a equation.
    Yes I can.

    ReplyDelete
  22. Equations have to be solved while expressions are to be expanded, simplified, etc.
    Variables have no fixed value while constants have a fixed value and will not change. Coefficients are constants merged with variables.

    ReplyDelete
  23. 1.An equation is the value of an expression with an equal sign. An expression is could be a simplified version of another equation but it doesn't have the variable.
    2.Yes. The letters are variables, the numbers that "sticks" to the variables are coefficients. Constants are numbers like 1,2,3,4,5 that do not have a varied value, like1 would forever 1
    a)coefficient:0.2,variable:m
    b)coefficient:-3,variable:p
    c)coefficient:-7/8,variable:q
    d)coefficient:1,variable:z
    e)coefficient:1/4,variable:x

    ReplyDelete
  24. Expressions are working without an answer, while equations are workings with answers.
    - Coefficient are numbers that are not constant and varies along with the variable.
    - Variables are represented by alphabets and can vary. They are not constant.
    - Constants are numbers with a constant value that would not change.
    Yes, I am able to.

    ReplyDelete