Take out debug prints and ... Test output...
extend tests to include input of 1/0 and a divide by zero

Divide by zero causes an exception as shown by Test output...
$ java -ea FractionCalculatorTest
FractionTestCalculator tests verbose output:
test "Simple parsing and operation: input of "1/2 * 3/4" should give "3/8". Actually "3/8" is output." passes.
test "Simple parsing and operation: input of "1/2 / 3/4" should give "2/3". Actually "2/3" is output." passes.
test "Simple parsing and operation: input of " 1/2   +  -1/4 " should give "1/4". Actually "1/4" is output." passes.
test "Simple parsing and operation: input of "1/2 - 3/4" should give "-1/4". Actually "-1/4" is output." passes.
test "Entering an invalid fraction input of "1/0" should produce an ERROR. Actually "
ERROR you have specified a fraction 1/0 with a zero denominator.
	Resetting calculator to its initial state (no operator and 0 as value)" is output." passes.
Exception in thread "main" java.lang.IllegalArgumentException: Invalid fraction with denominator 0.
	at Fraction.<init>(Fraction.java:17)
	at Fraction.divide(Fraction.java:102)
	at FractionCalculator.dealWithFraction(FractionCalculator.java:140)
	at FractionCalculator.fractionProcess(FractionCalculator.java:128)
	at FractionCalculator.process(FractionCalculator.java:83)
	at FractionCalculatorTest.simpleTests(FractionCalculatorTest.java:69)
	at FractionCalculatorTest.main(FractionCalculatorTest.java:16)