Verbal language and algebraic language
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  1. Translating from verbal lenguaje to algebraic lenguaje

    The word addition has the following meanings: make bigger, bigger than, more and to increase.

    The word subtraction refers to: minus, less than, difference, decrease and lose.

    In a multiplication we can also use the words: product, multiple, twice, double/triple, etc.

    In a division we use the following terms: quotient, to divide, divided by, half/third/third part, etc.

    In a verbal expression we can use the term “an ordinary number” It is written in algebraic form with the letter x or with another one, like a,n, etc.

    “The sum of two numbers” Represented by x  +  y

    “The difference between two numbers” Represented by x – y

    The product of two numbers. This is a multiplication and its representation is xy. Multiplication is represented as two letters who are joined.

    The quotient of two numbers. It is a division of x divided by y: x/y

    The result of the addition multiplied by the difference. Represented by two brackets

     (  )( ) The final result is (x+y)(x-y).

  A. Choose the correct answer: a, b, c.

  1. The sum of two numbers

    a.  x-y
    b.  x+y
    c.  xy


  2. The square of a number

    a.  x2
    b.  x / 2
    c.  2x


 3. Four times the square of a number

    a.  (4x)2
    b.  42 x
    c.  4(x)2


 4. The difference between the square of two numbers

    a.  x2 - y2
    b.  (x - y)2
    c.  2(x2 - y2)


 5. The four part of the cube of a number

    a.  4(x3)
    b.  x3 / 4
    c.  4 / x3


 6. The difference between two numbers divided by the sum

    a.  +(x - y)
    b.  2(x - y)
    c.  x-y / x+y


  2. Translating from algebraic lenguaje to verbal languaje

   We must learn to give a name to equations in a certain order.
       1º  3x2  The first operation is a multiplication of 3 for x squared or we can also say the triple. We write: the triple of the square of a number.
       2º 5(x+4)3 We can say: Five times the cube of the sum of a number and four.
       3º 2(a+b+c) The double of the sum of three different numbers.
       4º  √abc  The root of the result of three numbers.                     x
      5º  x/3  or  3  A third of a number.      
We must observe the main operation (it can be addition, difference, etc.) and later describe the variables in the algebraic expression.

  B. Choose the correct answer: a, b or c.

  1. Translate the algebraic expression to verbal language:  2x3

    a. The double of the square of a number
    b. The square of two multiplied by a number
    c. The cube of a number divided by two


  2. 6(x - 3)2

    a. The double of a number minus three squared to six
    b. The square of six multiplied by a number minus three
    c. Six times the square of the difference between a number and three


 3. x / 5

    a. Five times a number
    b. A fifth of a number
    c. A quint of a number


 4. x2 + y

    a. The sum of the square of a number and other number
    b. The double of the sum of two numbers
    c. The square of the sum of two numbers


 5. 3( a + b + c)

    a. The cube of the sum of three numbers
    b. The sum of the cube of three numbers
    c. The third of the sum of three different numbers


 6. x/3 - y

    a. The third of the difference of two numbers
    b. The difference of the third of two numbers
    c. The third of the difference of three numbers


  3. Numeric value

      We call numeric value of an algebraic expression to the result that we obtain doing the operations indicated in it, after changing every letter for their corresponding value.

      If letters are joined it means that they are in a multiplication. The multiplication sign is a dot ( . )      Example: Find the numeric value of 4a2b3c, knowing that a=2, b=3 y c=5.

      We must substitute letters for numeric values: 4 . 22. 33. 5

     Powers are found: 4 . 4 . 27. 5      The product is resolved: 2160   


  C. Choose the correct answer: a, b, c. You must do the operations in a piece of paper.

  1. Find the numeric value of the following algebraic expression: a2 - 2ab + b2, if a=4, b=2

    a. 16
    b. 36
    c. 4


  2. Numeric value of:  3a2b - 3ab2 + 5b3, if a=8, b=6

    a. 1 368
    b. 1 152
    c. 864


 3. Numeric value of:  -15a + 20b +3ab, if a=2, b=3

    a. 30
    b. 48
    c. 60


 4. Numeric value of:  x3 + 3x2y +3xy2 + y3, if x=5, y=4

    a. 729
    b. 425
    c. 304


 5. Find the numeric value of: 18abc -13ac + 8ab -5bc, if a=0, b=4, c=3

    a. 480
    b. 60
    c. 240


 6. Numeric value of:  5a + 3b -7c +2ab, if a=4, b=2, c=1

    a. 19
    b. 60
    c. 35


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