Problems on Division of Fractional Numbers

This topic would deal with problems on division of fractional number. We are familiar with the fact that division of fraction with another fraction involves multiplying the fraction with the reciprocal or multiplicative inverse of another fraction. The same concept would be utilized in story sums or problems on division of fractional numbers.

Here are few examples:

1. Rita bought 4 kgs of sugar for Rs. 1702/5 . Find the cost of 1 kg of sugar.

Solution:

Cost of 4 kg of sugar = Rs. 1702/5

Cost of 1 kg of sugar = Rs. 1702/5 ÷ 4

                               = 1702/5 ÷ 4/1

                               = 852/5 × 1/4

                               = 213/5

Therefore, Cost of 1 kg of sugar = Rs 423/5

Explanation:

Cost of 4 kgs sugar is given and here the sum requires to find out the cost of each kg of sugar. We know that the cost of 1 kg of sugar would be less than the cost of 4 kg of sugar. Therefore this cost of 4kg of sugar has to be divided to find out the cost of 1kg of sugar. That means we have to do Rs. 1702/5 ÷ 4 to get the answer of each kg of sugar that is Rs 423/5


2. In a school 3/5 of the students are boys. If there are 600 girls in the school then find the number of boys in the school.

Solution:

Let the total no. of students be 1

Fraction of boys = 3/5

Fraction of girls = 1 – 3/5

     = 2/5

Therefore, 2/5 of the students are girls = 600

Then total no. of students = 600 ÷ 2/5

          =600 × 5/2

          = 1500 students

Therefore, number of boys = 1500 – 600 = 900 girls

Explanation:

It is mentioned that in a school there are 600 girls and 3/5 of the students are boys. Here we assume the total no .of students be 1 as the total fraction is always considered as 1. Then if 3/5

Of the students are boys then we can easily say that 1 – 3/5 are girls. Now, this 2/5   is equivalent to 600 girls. Hence we need to find out the total no. of students first. Then from the total no. of students the no. of girls is subtracted to get the no. of boys.


3. A bar of chocolate of length 153/4 cm is divided into a number of pieces. Each piece is of 3/4 cm. Find the number of pieces of chocolate that can be cut from the bar of chocolate.

Solution:

Total length of a chocolate bar            = 153/4 cm

Length of each piece of chocolate bar = 3/4 cm

Therefore, total no. of pieces that can be cut = 153/4 ÷ 3/4

= 63/4 × 4/3

= 21 pieces

Therefore, total no. of pieces that can be cut from the bar of chocolate = 21 pieces

Explanation:

Here the total length of the chocolate bar is 153/4 cm and the length of each piece is given as 3/4

cm. So we have to find out that this chocolate bar can be divided into how many pieces. So we have to divide 153/4 ÷ 3/4  to get the answer as 21 pieces

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