Order of operations is not important to solve equations. It is a mere convention to help shorten, clarify, and disambiguate expressions that use . It could all be replaced by equivalent but ugly standard notation for functions.
For example the equation (2x2−3x+4)/2x=0 could be written as:
d(p(m(t(2,e(x,2)),t(3,x)),4),e(2,x))=0 where:
d(x,y)≡x/y
p(x,y)≡x+y
m(x,y)≡x−y
t(x,y)≡x×y
e(x,y)≡xy
Functional notation explicitly states the order in which the operations or functions are to be applied: no rules to specify the order are required.
Our standard infix notation, however, leaves an expression like x+y×z ambiguous – it requires a rule to state “multiplication before addition” for it to mean x+(y×z) rather than (x+y)×z . That rule is important to understand the meaning of the expression, but it could be replaced by fully parenthesising the expression or using
p(x,t(y,z)) rather than t(p(x,y),z)
It’s rather like boring prose verses beautiful poetry. Poetry is not essential or important per se, but the world would be a poorer place without it.
Answers & Comments
Answer:
because if you didn't follow the rules in the order of operations you might get the wrong answer in the the equation you are answering. :>
Step-by-step explanation:
#CarryOnLearning
Answer:
Order of operations is not important to solve equations. It is a mere convention to help shorten, clarify, and disambiguate expressions that use . It could all be replaced by equivalent but ugly standard notation for functions.
For example the equation (2x2−3x+4)/2x=0 could be written as:
d(p(m(t(2,e(x,2)),t(3,x)),4),e(2,x))=0 where:
d(x,y)≡x/y
p(x,y)≡x+y
m(x,y)≡x−y
t(x,y)≡x×y
e(x,y)≡xy
Functional notation explicitly states the order in which the operations or functions are to be applied: no rules to specify the order are required.
Our standard infix notation, however, leaves an expression like x+y×z ambiguous – it requires a rule to state “multiplication before addition” for it to mean x+(y×z) rather than (x+y)×z . That rule is important to understand the meaning of the expression, but it could be replaced by fully parenthesising the expression or using
p(x,t(y,z)) rather than t(p(x,y),z)
It’s rather like boring prose verses beautiful poetry. Poetry is not essential or important per se, but the world would be a poorer place without it.
Step-by-step explanation:
ctto:)