Given: Show all work: Each letter is an operand The operators and order of opera

Question

Given:

Show all work:

Each letter is an operand

The operators and order of operation is as follows from highest to lowest

$ Exponent

*, /, % Multiplication, division, remainder

+, - Addition, subtraction

(4 points each conversion)

Transform each of the following expressions to prefix then postfix

A - B + C

(A – B) / (C + D) $ E * F

(A – B) * (C $ (D + E) – F) + G

(A – ((( B + C) * (D + E) – F) * G)) $ (H + J)

(A / B) – ((C * D) + ( E / F))  

Transform each of the following prefix expressions to infix (USE PARENTHESES)

- + A B C

– A + B C

- - A + / $ B C D * - E F / G H I

- + $ A B C / D * / E F G

– A / B * C $ D E

Transform each of the following postfix expressions to infix (USE PARENTHESES)

A B – C +

A B C - +

A B + C - D E F + - $

A B + C – B A + C $ -

A B C D E + - $ * F G / -

Explanation / Answer

1) a ) A - B + C

Prefix : + - A B C

Postfix : A B - C +

b) (A – B) / (C + D) $ E * F

Prefix :* / - A B $ + C D E F

Postfix: A B- C D + $ E / F *

c) (A – B) * (C $ (D + E) – F) + G

Prefix : + * - A B - $ c +D E F G

Postfix : A B- C $ D E + – F * G +

d) (A – ((( B + C) * (D + E) – F) * G)) $ (H + J)

Prefix :$ - A * - *+ B C + D E F G + H J

Postfix :A – B C + D E + – F * G * $ H J +

e) (A / B) – ((C * D) + ( E / F))

Prefix : - / A B + * C D / E F

Postfix : A B / – C D * E F / +

2 ) a) - + A B C

infix : ((A+B)-C)

b) - A + B C

infix : (A-(B+C))

c) - A + / $ B C D * E F / G H I

infix : The given prefix expression is Invalid , hence cannot be converted to infix

d) - + $ A B C / D * / E F G

infix : (((A$B)+C)-(D/((E/F)*G)))

e) – A / B * C $ D E

infix : (A-(B/(C*(D$E))))

3) a) A B – C +

Infix : (A-B) + C

b) A B C - +

Infix : A + B - C

c) A B + C - D E F + - $

infix : (A + B - C) $ (D - (E + F))

d) A B + C – B A + C $ -

infix : (A+B-C ) $ (B+A-C)

e) A B C D E + - $ * F G / -

infix : A * B $ (C - (D + E)) - F / G

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