Question

The sum of the lengths of three ropes is 12 m. If one rope is 5 2/15 and another is 3 3/10 m long, find the length of the third rope

Answer 1

add the lengths of both 1 and 2 ropes and than subtract it from the length of three ropes

Answer 2

Answer:

3 17/30

Step-by-step explanation:

⇒Given

• The sum of the lengths of three ropes is 12 m

• One rope = 5 2/15
• Second rope = 3 3/10 m
• Third rope =  12 - 5 2/15 + 3 3/10

⇒Method

5 5/12 + 3 3/10 + $x$ = 12 m

∴ $x$ = 12 - 5 2/15 + 3 3/10

Conversion into improper fraction

5 5/12 = 77/15

3 3/10 = 33/10

So, we have to do $77/15 +33/10 =$

We have to find the LCM of denominators to find the sum of two fractions  

LCM= 30

77/15 x 2 = 154/30

33/10 x 3 = 99/30

⇒ 154/30 + 99/30 = 253/30

253/30 -12/1 =

253/30 - 360/30= 107/30

Now, we have to convert 107/30 into a mixed fraction

Conversion into mixed fraction

107/30 = 3 17/30

Verification

5 2/15 + 3 3/10 + 3 17/30 = 12 m

Conclusion

∴The length of the third rope is 3 17/30