Question

From a sack of potatoes weighing $120$kg, a merchant sells portion weighing $6$kg, $5\dfrac{1}{4}$kg, $9\dfrac{1}{2}$kg and $9\dfrac{3}{4}$kg respectively.
1.How many kg did he sell?
2.How many kg are still left in a sack?

Answer 1

Hint: Here, From a sack of potatoes weighing $120$kg, a merchant sells portion weighing $6$kg, $5\dfrac{1}{4}$kg, $9\dfrac{1}{2}$kg and $9\dfrac{3}{4}$kg respectively. So to find how many kg he sells add all the weighing portions and for left in sack, subtract $120$kg and weigh portions.

Complete step-by-step answer:
Here, From a sack of potatoes weighing $120$kg, a merchant sells portion weighing $6$kg, $5\dfrac{1}{4}$kg, $9\dfrac{1}{2}$kg and $9\dfrac{3}{4}$kg respectively.
So now to find how many kg he sells let us add all the weighing portions.
Potatoes sold by merchant$=6+5\dfrac{1}{4}+9\dfrac{1}{2}+9\dfrac{3}{4}$
Now solving the mixed fraction in simple manner we get,
Potatoes sold by merchant$=6+\dfrac{21}{4}+\dfrac{19}{2}+\dfrac{39}{4}$.
Now taking LCM we get,
Potatoes sold by merchants$=\dfrac{24+21+38+39}{4}$.
Potatoes sold by merchants$=\dfrac{122}{4}=\dfrac{61}{2}$kg.
Now to find the potatoes left in the sack subtract the weighing portion from $120$kg.
Potatoes left in the sack$=120-\dfrac{61}{2}$.
Simplifying in simple manner we get,
Potatoes left in the sack$=\dfrac{179}{2}$kg.
So we get both the answers.
The potatoes sold by merchants and left in sacks are $\dfrac{61}{2}$kg and $\dfrac{179}{2}$kg.

Additional information:
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers. LCM denotes the least common factor or multiple of any two or more given integers. LCM is used in the case when the denominators of the fractions are different. While performing any arithmetic operations such as addition, subtraction with fractions, LCM is used to make the denominators as the same numbers. This process makes the simplification process easier.

Note: In the question it must be clear that what is asked. The concept of LCM must be cleared. A common multiple is a number which is a multiple of two or more numbers. LCM denotes the least common factor or multiple of any two or more given integers. Also, mixed fraction conversion should not be mistaken.