Properties of Addition of Fractions

The associative and commutative properties of natural numbers hold good in the case of fractions also.

I: Commutative Property of Addition of Fractions: 

While adding two fractions we may add them in either order. The sum of the fractions remains the same.

                       i.e., \(\frac{2}{3}\) + \(\frac{1}{4}\) = \(\frac{1}{4}\) + \(\frac{2}{3}\)

II: Associative Property of Addition of Fractions:

While adding more than two fractions, we may add them in any order; the sum of the fractions remains the same.

              i.e., [\(\frac{2}{5}\) + \(\frac{3}{4}\)] + \(\frac{1}{3}\) = \(\frac{2}{5}\) + [\(\frac{3}{4}\) + \(\frac{1}{3}\)]

III: Zero Property of Addition of Fractions:

If zero is added to any fraction we get back the same fraction.

Questions and Answers on Properties of Addition of Fractions:

I. Fill in the Blanks:

(i) \(\frac{3}{5}\) + \(\frac{1}{4}\) = \(\frac{1}{4}\) + ______

(ii) \(\frac{1}{6}\) + ______ = \(\frac{1}{8}\) + ______

(iii) \(\frac{7}{15}\) + \(\frac{3}{5}\) + \(\frac{2}{9}\) = \(\frac{2}{9}\) + ______ + \(\frac{3}{5}\)

(iv) \(\frac{9}{20}\) + \(\frac{4}{15}\) + ______ = \(\frac{3}{5}\) + \(\frac{9}{20}\) + \(\frac{4}{15}\)

Answer:

I. (i) \(\frac{3}{5}\)

(ii) \(\frac{1}{8}\); \(\frac{1}{6}\)

(iii) \(\frac{7}{15}\)

(iv) \(\frac{3}{5}\)

II. Verify the following (show that left hand side = right hand side)

(i) \(\frac{3}{5}\) + \(\frac{2}{8}\) = \(\frac{2}{8}\) + \(\frac{3}{5}\)

(ii) [\(\frac{1}{6}\) + \(\frac{2}{3}\)] + \(\frac{1}{4}\) = \(\frac{1}{6}\) + [\(\frac{2}{3}\) + \(\frac{1}{4}\)]

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