What is expression decoding? (with examples)

The expression decoding refers to the way of verbally expressing a mathematical expression. In mathematics, a expression, also called mathematical expression, it is a combination of coefficients and literal parts joined through other mathematical signs (+, -, x, ±, /, [],), to form a mathematical operation.

In simpler words, the coefficients are represented by numbers, while the literal part is made up of letters (generally the last three letters of the alphabet, a, b and c, are used to designate the literal part).

In turn, these "letters" represent quantities, variables and constants to which a numerical value can be assigned..

Mathematical expressions are made up of terms, which are each of the elements that are separated by operation symbols. For example, the following mathematical expression has four terms:

5x^two + 10x + 2x + 4

It should be noted that expressions can be constituted only by coefficients, by coefficients and literal parts and only by literal parts.

For example:

25 + 12

2x + 2y (algebraic expression)

3x + 4 / y + 3 (irrational algebraic expression)

x + y (integer algebraic expression)

4x + 2y^two (integer algebraic expression)

Decoding mathematical expressions 

Decoding Simple Mathematical Expressions 

1. a + b: The sum of two numbers

For example: 2 + 2: The sum of two and two

2. a + b + c: The sum of three numbers

For example: 1 + 2 + 3: The sum of one, two and three

3. a - b: The subtraction (or difference) of two numbers

For example: 2 - 2: The subtraction (or difference) of two and two

4. a x b: The product of two numbers

For example: 2 x 2: The product of two and two

5. a ÷ b: The quotient of two numbers

For example: 2/2: The quotient of two and two

6. 2 (x): Double a number

For example: 2 (23): Double 23

7. 3 (x): Triple a number

For example: 3 (23): Triple 23

8. 2 (a + b): Double the sum of two numbers

For example: 2 (5 + 3): Double the sum of five and three

9. 3 (a + b + c): Triple the sum of three numbers

For example: 3 (1 + 2 + 3): Triple the sum of one, two and three

10. 2 (a - b): Double the difference of two numbers

For example: 2 (1 - 2): Double the difference of one and two

11. x / 2: Half of a number

For example: 4/2: Half of four

12. 2n + x: The sum of twice a number and another number

For example: 2 (3) + 5: The sum of the double of three and five

13. x> y: “X” is greater than “ye”

For example: 3> 1: Three is greater than one

14. x < y : “Equis” es menor que “ye”

For example: 1 < 3 : Uno es menor que tres

15. x = y: "X" is equal to "ye"

For example: 2 x 2 = 4: The product of two and two equals four

16. x^two : The square of a number or a number squared

For example: 5^two : The square of five or five squared

17. x³ : The cube of a number or a number cubed

For example: 5³ : The cube of five or five cubed

18. (a + b) ^two : The square of the sum of two numbers

For example: (1 + 2) ^two : The square of the sum of one and two

19. (x - y) / 2: Half the difference of two numbers

For example: (2 - 5) / 2: Half the difference of two and five

20. 3 (x + y) ^two : Triple the square of the sum of two numbers

For example: 3 (2 + 5) ^two : The triple of the block of the sum of two and five

21. (a + b) / 2: The semi-sum of two numbers

For example: (2 + 5) / 2: The semi-sum of two and five

Decoding algebraic expressions 

1. 2x⁵ + 7 / y + 9: [Two X's raised to five] plus [seven over ye] plus [nine]

2. 9 x + 7y + 3 x⁶ - 8 x³ + 4 and: [Nine Xs] plus [seven and e] plus [three X to the sixth] minus [eight X to the 3] plus [four and the]

3. 2x + 2y: [Two Xs] plus [Two Ye]

4. x / 2 - y⁵ + 4y⁵ + 2x^two : [x over 2] minus [ye to five] plus [four ye to five] plus [two xs squared]

5. 5/2 x + y^two + x: [Five over two x's] plus [ye squared] plus [x's]

Decoding polynomials 

1. 2x⁴ + 3x³ + 5x^two + 8x + 3: [Two of Xs raised to four] plus [Three of Xs raised to three] plus [Five of Xs squared] plus three

2. 13y⁶ + 7y⁴ + 9y³ + 5y: [Thirteen of ye to six] plus [seven of ye to four] plus nine of ye to three] plus [five of ye]

3. 12z8 - 5z6 + 7z5 + z4 - 4z3 + 3z2 + 9z: [Twelve zeta to eight] minus [five zeta to six] plus [seven zeta to five] plus [zeta to four ] minus [four zeta cubed] plus [three zeta squared] plus [nine zeta]

References 

1. Wrinting expressions with variables. Retrieved on June 27, 2017, from khanacademy.org.
2. Algebraic expressions. Retrieved on June 27, 2017, from khanacademy.org.
3. Comprehension of algebraic expressions by experienced users of mathematics. Retrieved on June 27, 2017, from ncbi.nlm.nih.gov.
4. Writing mathematical expressions. Retrieved on June 27, 2017, from mathgoodies.com.
5. Teaching arithmetic and algebraic expressions. Retrieved on June 27, 2017, from emis.de.
6. Expressions (mathematics). Retrieved on June 27, 2017, from en.wikipedia.org.
7. Algebraic expressions. Retrieved on June 27, 2017, from en.wikipedia.org.