Question

A cloth of \[\dfrac{{13}}{4}\] metres long is cut into strips $ \dfrac{1}{{12}} $ Metres long to make bandages. How many bandages were made ?

Answer 1

Hint: Here, before solving the problem, we need to have a clarity of what is the main material that has been provided and how long it is. Also the required product and its dimensions.
We have been provided with the material which is a \[\dfrac{{13}}{4}\]metres cloth which is the main material and we have to make X number of bandages $ \dfrac{1}{{12}} $ metres long each.

Complete step-by-step answer:
In such examples, to find out the number of products out of given material we divide the dimensions of the helping material with the actual dimensions of the product.
Let the number of bandages obtained be X.
The length of the helping material, here the length of the cloth is \[\dfrac{{13}}{4}\]metres.
The length of the product required, here the bandages is $ \dfrac{1}{{12}} $ metres.
Mathematically we put it as follows,
Number of bandages obtained\[ = \] length of the helping material\[/\] length of the product required
Here,
 $ X = \dfrac{{13}}{4} \div \dfrac{1}{{12}} $
Rearranging the terms for simplifying the above equation we get,
 $ \Rightarrow X = \dfrac{{13}}{4} \times \dfrac{{12}}{1} $
 $ \Rightarrow X = 13 \times 3 $
 $ \therefore X = 39 $
Thus, we have obtained the value of X which is \[39.\]
Here we have assumed X to be the number of bandages obtained from \[\dfrac{{13}}{4}\]metres long cloth and each bandage to be of the length $ \dfrac{1}{{12}} $ metres long.
Therefore, we can get 39 bandages of length $ \dfrac{1}{{12}} $ metres from \[\dfrac{{13}}{4}\]metres long cloth.

Note: 1. Solving these types of problems can be tricky and might lead to the mistake in understanding the given data and the required data.
2. Students should not make silly mistakes while multiplying and dividing fractions.
3. Students should also keep in mind the units of the given data.