Question

If p/q = 2/3 and r/s = 4/3, show that division is not commutative. Also show that their subtraction is not commutative.

Answer 1

division
p/q ÷r/s =p/q×r/s
2/3÷4/3=2×3/3×4=1/2.
r/s÷p/q=r/s×p/q
4/3÷2/3=4×3/2×3=2
therefore commutative property can't hold for
division.
subtraction:
2-4/3=-2/3
4-2/3=2/3
therefore commutative property can't hold for
subtraction

Answer 2

Division
p/q÷r/s =p/q×r/s
2/3÷4/3=2×3/3×4=1/2.
r/s÷p/q=r/s×q/p
4/3÷2/3=4/3×3/2=2
Therefore commutative property can't hold for
division.
Subtraction:
p/q-r/s=r/s-p/q
2/3-3/4=3/4-2/3
-1/12=1/12
Therefore commutative property can't hold for
subtraction.