Question

A clerk sold three pieces of one type of ribbon to different customers. One piece was 1 StartFraction 11 Over 27 EndFraction
yards​ long, another was 6 and three fourths
yards​ long, and the third was 17 and four ninths
yards long. What was the total length of that type of ribbon​ sold?

Answer 1

Answer:

Let’s assume,  

The length of the first piece of ribbon be “L1” = $1\frac{11}{27}$ yards long

The length of the second piece of the same type of ribbon be “L2” = $6\frac{3}{4}$  yards long

The length of the third piece of the same type of ribbon be “L3” = $17\frac{4}{9}$ yards long

Now, lets first convert the mixed fractions into fractions:

i) $1\frac{11}{27}$ = 1*27+11 = $\frac{38}{27}$

ii) $6\frac{3}{4}$ = 4*6+3 = $\frac{27}{4}$

iii) $17\frac{4}{9}$ = 9*17+4 = $\frac{157}{9}$

Therefore,  

The total length of the type of ribbon sold was,

= L1 + L2 + L3

=  $1\frac{11}{27}$ + $6\frac{3}{4}$ + $17\frac{4}{9}$

= $\frac{38}{27}$  + $\frac{27}{4}$  + $\frac{157}{9}$ …. [from (i), (ii) & (iii)]

= $\frac{152+728+1884}{108}$

= $\frac{2765}{108}$  yards long

Now, again let’s convert the fraction into a mixed fraction:  

108)2765(25

       216

     -------------

          605

          540

     ----------------

            65

     -----------------

Thus, the total length of that type of ribbon sold was $25\frac{65}{108}$ yards long.