Question

It takes \[\dfrac{3}{5}\] feet of ribbon to make a pin. You have 9 feet of ribbon. How many pins can you make?

Answer 1

Hint: A ratio is a mathematical expression written in the form of \[a:b\] , where a and b are any integers and b is not equal to 0 and it expresses a fraction. To find the number of pins which are to be made in 9 feet of ribbon, we need to consider to the given data that, to make 1 pin it takes \[\dfrac{3}{5}\] feet of ribbon, hence consider the given data and then finding the unknown variable i.e., number of pins to be made using 9 feet of ribbon.

Complete step by step solution:
Given,
It takes \[\dfrac{3}{5}\] feet of ribbon to make a pin i.e.,
 \[ \dfrac{3}{5}\] feet = 1 pin.
Hence, we need to find for 9 feet of ribbon how many pins we can make i.e.,
 \[ \Rightarrow \] 9 feet = x pins.
Let, the number of pins be x and to find out how many pins(x) we need to divide the total length by the length of the pin i.e.,
 \[x = 9 \div \dfrac{3}{5}\]
This, expression is same as:
 \[ x = 9 \times \dfrac{5}{3}\]
 \[ \Rightarrow x = \dfrac{{9 \times 5}}{3}\]
Multiply and evaluate the terms, we get:
 \[ \Rightarrow x = \dfrac{{45}}{3}\]
 \[ \Rightarrow x = 15\]
Therefore, 15 pins to be made using 9 feet of ribbon.
So, the correct answer is “15”.

Note: The ratio should exist between the quantities of the same kind. While comparing two things, the units should be similar. There should be significant order of terms and the comparison of two ratios can be performed, if the ratios are equivalent like the fractions. Hence, in this way we need to solve the question, comparing with the given data.