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**Question:**

A steel rod is 12 ⅞ meters long.From this two pieces,one 3 ¼ meters long and another 4 ⅔ meters long are cut off. What is the length of the remaining part of the rod?

Basic idea:

In this problem we have 12 ⅞ meter steel rod.We are cutting these rod as two pieces one is 3 ¼ m long and other is 4 ⅔ m long.Now we need to find the remaining measurement of steel rod.To solve this problem first we have to add the measurement of two pieces and then we have to subtract them from the original length of rod.

**Solution:**

Original length of steel rod = 12 ⅞ meter

Length of rod which had been cut = 3 ¼ + 4 ⅔

First we have to change these mixed fraction in to improper fraction

= (12+1)/4 + (12+2)/3

= (13/4) + (14/3)

Now we have to take L.C.M for the different denominators 4 and 3

L.C.M of 4 and 3 is 12

= (13/4) x (**3/3**) + (14/3) x (**4/4**)

= (39/12) + (56/12)

= (39 + 56) /12

= 95/12

Length of remaining rod = length of original rod - Length of rod which had been cut

= 12 ⅞ - (95/12)

= (96+7)/8 - (95/12)

= (103/8) - 95/12

Here L.C.M of 8 and 12 is 24

= (103/8) x (**3/3**) - (95/12) x (**2/2**)

= (309/24) - (190/24)

= (390-190)/24

= 200/24

If we simplify this we will get

= 25/3

Therefore the remaining length of rod is 25/3 m

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