Question

Verify associativity of multiplication of rational numbers for the following:
a) 1/2 , 3/4 , 5/6          b) 3/7 , 5/6 , 14/ 2​

Answer 1

verify both by associative property

a*(b*c) = (a*b)*c

1) 1/2*(3/4*5/6)= 1/2*15/24

= 15/48

(1/2*3/4)*5/6= 3/8*5/6

=15/48

hence verified

similarly solve part 2

Answer 2

Answer:

Step-by-step explanation:

Given set of rational numbers are

a)) $\frac{1}{2} , \frac{3}{4} , \frac{5}{6}$         b) $\frac{3}{7} , \frac{5}{6} , \frac{14}{2}$

To verify the associativity of multiplication

Recall the concepts

If a,b,c are any three rational numbers, then the associative property  of multiplication of rational numbers are given by

a(bc) = (ab)c

Solution

a) $\frac{1}{2} , \frac{3}{4} , \frac{5}{6}$

Here let us take a = $\frac{1}{2}$, b = $\frac{3}{4}$ and c = $\frac{5}{6}$

bc = $\frac{3}{4} X\frac{5}{6}$

= $\frac{5}{8}$

a(bc) = $\frac{1}{2} X \frac{5}{8}$ = $\frac{5}{16}$

ab = $\frac{1}{2}X\frac{3}{4}$

=$\frac{3}{8}$

(ab)c = $\frac{3}{8} X\frac{5}{6}$ =  $\frac{5}{16}$

Hence the associative property of multiplication a(bc) = (ab)c is proved

b)  $\frac{3}{7} , \frac{5}{6} , \frac{14}{2}$

Here let us take a = $\frac{3}{7}$, b =  $\frac{5}{6}$  and c =$\frac{14}{2}$

bc = $\frac{5}{6}} X\frac{14}{2}$

= $\frac{35}{6}$

a(bc) =$\frac{3}{7}X \frac{35}{6} = \frac{5}{2}$

ab =$\frac{3}{7} X \frac{5}{6} =\frac{5}{14}$

(ab)c = $\frac{5}{14} X\frac{14}{2} = \frac{5}{2}$

Hence the associative property of multiplication a(bc) = (ab)c is verified.

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