you'd be changing the size of the piece (or pieces) ______________ Here is an analogy which may or may not help: Mary has 3 cats, Don has 4 cats. How many cats do they have in all? The answer is 7 cats, not 7 ccaattss. John has 1 quarter. Marie has 1 quarter (a quarter is 1/4 of a dollar). Together they have 2 quarters, not 2 eighths.
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it stay the same when you subtract fractions and when you add fractions.
You need a common denominator in order to add or subtract fractions.
You DO need a common denominator to add, subtract, or compare fractions. You DO NOT need a common denominator to multiply or divide fractions.
Unless you are using a calculator that adds them for you, it is much harder to add fractions with uncommon denominators. Having the same denominator allows you to only have to add the numerators for your answer.
You first convert them to equivalent fractions with a common denominator. Or you convert them to decimal fractions.