# Problems on Division of Decimal Fractions

Here in this topic deals with division of decimals fractions in the form of story sums. A story will be given along with the sum and we need to determine what operation we need to perform to solve the problem along with writing proper statements.

Here are few examples on problems on division of decimals to illustrate the topic:

1. If the cost of 5 notebooks is $85.85. Find the cost of 1 notebook. Solution: Cost of 5 notebooks =$85.85

Cost of 1 notebook =  $85.85 ÷ 5 Therefore, the cost of one note book is$17.17

Here the cost of 5 notebooks is given and we need to find the cost of 1 notebook. Hence we need to divide the cost of 5 note books by 5 to get the cost of 1 notebook.

2. There are few bags of rice weighing 7.3 kg each. Now on weighing all the bags it is found that the total weight of all the bags is 65.7 kg. Find the number of bags of rice.

Solution:

Total weight of all the bags of rice = 65.7 kg

Weight of each bag of rice            =   7.3 kg

Therefore, no. of bags of rice        = 65.7 ÷ 7.3 kg

(Here there is equal no. of decimal points in both the divisor and the dividend so we will divide both the numbers by 10 as there is 1 place after the decimal point in the divisor

65.7/10 ÷ 7.3/10

As we have learnt in other subtopics while dividing a fraction by another fraction is that a fraction is multiplied by the reciprocal of another fraction likewise we will do so

= 657/10 × 10/73

= (657 × 10) / (10 × 73)

On changing it into lowest terms we get,

= 657/73

Now in the normal way of division we will divide both the numbers)

= 657 ÷ 73

Therefore, there are 9 bags of rice weighing 7.3 kg each.

Here in this sum the total weight of few bags of rice is given and weight of 1 bag of rice is also given so we need to divide the total weight of all the bags by the weight of one bag to get the total no. of bags of rice.

3. If the product of two numbers is 153.9. If one number is 10. Find the other number.

Solution:

The product of two numbers = 153.9

One number = 10

Therefore other no. is 153.9 ÷ 10

= 15.39

The other number is 15.39

Here we are not doing actual division as it is a division by 10 that means 1 zero hence the decimal point in the dividend will move by one place to the left to get the answer.

4. 25.5 m long rope is cut into five pieces. Find the length of each piece.

Solution:

Length of rope = 25.5 m

No. of pieces = 5

Length of each piece = 25.5 ÷ 5

Therefore, the length of each piece = 5.1 m

Here the total length of rope is given 25.5 m and it is cut into 5 pieces. Hence in order to find the length of each piece we have to divide 25.5 by 5.

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