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

4th Grade Math Activities

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