Question

Identify the operations (addition,subtraction,multiplication,division) in forming the following expressions and tell how expressions have been formed.
$
  \left( a \right)z + 1,z - 1,y + 17,y - 17\,\,\,\,\,\,\,\left( b \right)17y,\dfrac{y}{{17}},5z \\
  \left( c \right)2y + 17,2y - 17\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( d \right)7m, - 7m + 3, - 7m - 3 \\
$

Answer 1

Hint:
The operations addition , subtraction, multiplication, division will be used. If there is + symbol it is addition. If there is a “-“ symbol it is subtraction. If there is “.” Or no symbol between the one constant and variable it is multiplication. If there is “/” symbol it is division.

Complete Step by Step Solution:
The objective of the problem is to identify the operations in forming the given expressions .
The given expressions are
$
  \left( a \right)z + 1,z - 1,y + 17,y - 17 \\
  \left( b \right)17y,\dfrac{y}{{17}},5z \\
  \left( c \right)2y + 17,2y - 17 \\
  \left( d \right)7m, - 7m + 3, - 7m - 3 \\
$
Here in the expressions given operations are addition , subtraction , multiplication , division.
Now let us see how the given expressions are formed by using given operations.
Given expressions $z + 1,z - 1,y + 17,y - 17$
The expression$z + 1$ is formed with one variable and one constant. Here the variable is “z” and the constant is 1. The variable and constant are combined with the operation addition (+).
Therefore , the observed operation in $z + 1$ is addition.
The expression $z - 1$ is formed with one variable and one constant. Here the variable is “z” and the constant is 1. The variable and constant are combined with the operation subtraction (-).
Therefore , the observed operation in $z - 1$ is subtraction.
The expression $y + 17$ is formed with one variable and one constant. Here the variable is “y” and the constant is 17. The variable and constant are combined with the operation addition (+).
Therefore , the observed operation in $y + 17$ is addition.
The expression $y - 17$ is formed with one variable and one constant. Here the variable is “y” and the constant is 17. The variable and constant are combined with the operation subtraction(-).
Therefore , the observed operation in $y - 17$ is subtraction.
Given expressions $17y,\dfrac{y}{{17}},5z$
The expression$17y$ is formed with one variable and one constant. Here the variable is “y” and the constant is 17. The variable and constant are combined with the operation multiplication. Actually the multiplication is denoted with dot(.) or star symbol(*) or with an into symbol$\left( \times \right)$ or with no symbol just like $17y$.
Therefore , the observed operation in $17y$ is multiplication.
The expression $\dfrac{y}{{17}}$ is formed with one variable and one constant. Here the variable is “y” and the constant is 17. The variable and constant are combined with the operation division.
Therefore , the observed operation in $\dfrac{y}{{17}}$ is division.
The expression $5z$ is formed with one variable and one constant. Here the variable is “z” and the constant is 5. The variable and constant are combined with the operation multiplication. Actually the multiplication is denoted with dot(.) or star symbol(*) or with an into symbol$\left( \times \right)$ or with no symbol just like $5z$.
Therefore , the observed operation in $5z$ is multiplication.
Given expressions $2y + 17,2y - 17$
The expression$2y + 17$ is formed with one variable and two constants. Here the variable is “y” and the constants are 2 and 17. The constant 2 and variable y are combined with operation multiplication. 2y and constant 17 are combined with the operation addition.
Therefore , the observed operations in $2y + 17$ are multiplication and addition.
The expression$2y - 17$ is formed with one variable and two constants. Here the variable is “y” and the constants are 2 and 17. The constant 2 and variable y are combined with operation multiplication. 2y and constant 17 are combined with the operation subtraction.
Therefore , the observed operations in $2y - 17$ are multiplication and subtraction.
Given expressions $7m, - 7m + 3, - 7m - 3$
The expression $7m$ is formed with one variable and one constant. Here the variable is “m” and the constant is 7. The variable and constant are combined with the operation multiplication. Actually the multiplication is denoted with dot(.) or star symbol(*) or with an into symbol $\left( \times \right)$ or with no symbol just like $7m$.
Therefore , the observed operation in $7m$ is multiplication.
The expression$ - 7m + 3$ is formed with one variable and two constants. Here the variable is “m” and the constants are -7 and 3. The constant -7 and variable m are combined with operation multiplication. -7m and constant 3 are combined with the operation addition.
Therefore , the observed operations in $ - 7m + 3$ are multiplication and addition.
The expression$ - 7m - 3$ is formed with one variable and two constants. Here the variable is “m” and the constants are -7 and 3. The constant -7 and variable m are combined with operation multiplication. -7m and constant 3 are combined with the operation subtraction.
Therefore , the observed operations in $ - 7m - 3$ are multiplication and subtraction.

Note:
Algebraic expressions are used to represent a bunch of numbers from a single variable. As in this question we used to operate them with different operations. Whole algebra is based on this small technique.