Word Problems in Fractions 1

In most life situations involving fractions, usually one of the numbers would be a fraction & the other would be a whole number or a decimal number. A typical example is given below.

The price label on a clock in a shop said Rs 200. Since a Diwali sale was going on, the clock was available for 3/4thof the list price. What was the actual price at which it was sold?

Life situations involving operations with 2 fractions are very rare. But it is a good exercise in understanding basic concepts about fractions, to try and frame some word problems.

Addition

Let us take ¾ + ½. For reasons, explained in an earlier chapter, this situation is best illustrated with discrete representation. A typical problem would be as follows.

A pizza parlor sells only 6” pizzas that too divided into 4 pieces. Each pizza costs Rs 200. Ram likes pizzas and wants to order ¾ of a pizza. Shyam only wants ½ a pizza. How much pizza would they order and how much would they pay for it?

The solution is that Ram needs 3 slices and Shyam needs 2 slices. Hence together they need 5 slices. This is equal of 5/4 or 1 ¼ of a pizza. Hence, they would have to pay Rs 250.

We can see that the above problem imposes many restrictions (only one size of pizza that too divided into only 4 pieces) which would be unrealistic in a real-life situation. Situations with unlike fractions (like 1/3 + 1/7) would be too unrealistic.

Subtraction

Let us take ¾ - ½. Here again the situation is best illustrated with discrete representation. A typical problem would be as follows.

Solution – we assume that the original chocolate bar was divided into 8 (3/4thof 8) portions. So Ram took 6 portions to school. He gave 4 (1/2 of 8) portions to his friends. So he was left with 2 portions which is ¼ th of the original bar.

A realistic scenario would be Ram sharing ½ of the chocolate from his share and not ½ of the original chocolate. But that would make it a multiplication problem! We will see it in detail in the next chapter.

Hence we see that fraction subtraction problems are very unrealistic.

The reality of fraction operations

We deal with situations involving fraction additions and subtractions, on a daily basis. But we do these with physical materials and on a subjective & approximate manner. When we share a sandwich between 2 friends, we do not argue whether they are exactly equal!

But we have seen above, that representing these transactions in exact mathematical format comes out as “artificial”. Hence formal calculations with fractions are done only for “official” purposes like interest calculations & property demarcations.