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.

 Add: $$\frac{2}{3}$$ + $$\frac{1}{4}$$ L.C.M. of 3, 4 is 12 $$\frac{2}{3}$$ + $$\frac{1}{4}$$ = $$\frac{8}{12}$$ + $$\frac{3}{12}$$ = $$\frac{11}{12}$$ Add:$$\frac{1}{4}$$ + $$\frac{2}{3}$$ L.C.M. of 4, 3 is 12 $$\frac{1}{4}$$ + $$\frac{2}{3}$$ = $$\frac{3}{12}$$ + $$\frac{8}{12}$$ = $$\frac{11}{12}$$

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.

 Add:[$$\frac{2}{5}$$ + $$\frac{3}{4}$$] + $$\frac{1}{3}$$     L.C.M. of 5 and 4 is 20. [$$\frac{2}{5}$$ + $$\frac{3}{4}$$] + $$\frac{1}{3}$$ = [$$\frac{8}{20}$$ + $$\frac{15}{20}$$] + $$\frac{1}{3}$$ [$$\frac{2}{5}$$ + $$\frac{3}{4}$$] + $$\frac{1}{3}$$ = $$\frac{23}{20}$$ + $$\frac{1}{3}$$ L.C.M. of 20 and 3 is 60.= $$\frac{69}{60}$$ + $$\frac{20}{60}$$ = $$\frac{89}{60}$$ = 1$$\frac{29}{60}$$ Add:$$\frac{2}{5}$$ + [$$\frac{3}{4}$$ + $$\frac{1}{3}$$]L.C.M. of 4 and 3 is 12.= $$\frac{2}{5}$$ + [$$\frac{9}{12}$$ + $$\frac{4}{12}$$]= $$\frac{2}{5}$$ + $$\frac{13}{12}$$L.C.M. of 5 and 12 is 60. = $$\frac{24}{60}$$ + $$\frac{65}{60}$$= $$\frac{89}{60}$$ = 1$$\frac{29}{60}$$

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.

 Add:$$\frac{1}{2}$$ + 0 = $$\frac{1}{2}$$ + $$\frac{0}{2}$$ = $$\frac{1 + 0}{2}$$ = $$\frac{1}{2}$$ Therefore, $$\frac{1}{2}$$ + 0 = 0 + $$\frac{1}{2}$$ = $$\frac{1}{2}$$ Add:$$\frac{5}{6}$$ + 0 = $$\frac{5}{6}$$ + $$\frac{0}{6}$$ = $$\frac{5 + 0}{6}$$ = $$\frac{5}{6}$$ Therefore, $$\frac{5}{6}$$ + 0 = 0 + $$\frac{5}{6}$$ = $$\frac{5}{6}$$

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

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

You might like these

• Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerator < denominator). Two parts are shaded in the above diagram.

• Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

• Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with respect to the whole shape in the figures from (i) to (viii) In; (i) Shaded

• Subtraction of Fractions having the Same Denominator | Like Fractions

To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numerators of the fractions.

• Comparison of Like Fractions | Comparing Fractions | Like Fractions

Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example $$\frac{7}{13}$$ > $$\frac{2}{13}$$ because 7 > 2. In comparison of like fractions here are some

• Comparison of Fractions having the same Numerator|Ordering of Fraction

In comparison of fractions having the same numerator the following rectangular figures having the same lengths are divided in different parts to show different denominators. 3/10 < 3/5 < 3/4 or 3/4 > 3/5 > 3/10 In the fractions having the same numerator, that fraction is

• Like and Unlike Fractions | Like Fractions |Unlike Fractions |Examples

Like and unlike fractions are the two groups of fractions: (i) 1/5, 3/5, 2/5, 4/5, 6/5 (ii) 3/4, 5/6, 1/3, 4/7, 9/9 In group (i) the denominator of each fraction is 5, i.e., the denominators of the fractions are equal. The fractions with the same denominators are called

• Fraction of a Whole Numbers | Fractional Number |Examples with Picture

Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One part is shaded, i.e., one-fourth of the shape is shaded and three

• Worksheet on Equivalent Fractions | Questions on Equivalent Fractions

In worksheet on equivalent fractions, all grade students can practice the questions on equivalent fractions. This exercise sheet on equivalent fractions can be practiced by the students to get more ideas to change the fractions into equivalent fractions.

In worksheet on addition of fractions having the same denominator, all grade students can practice the questions on adding fractions. This exercise sheet on fractions can be practiced by the students to get more ideas how to add fractions with the same denominators.