Question

What is \[\dfrac{3}{4}\] divided by \[\dfrac{2}{5}\]?

Answer 1

Hint: For the above problem, we should know how to divide fractions. Let we have two fractions \[\dfrac{a}{b}\And \dfrac{c}{d}\], and we are asked to divide the first fraction by the second fraction. Algebraically we need to calculate the value of \[\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}\]. Here, we need to know that this type of expression can be simplified as \[\dfrac{a}{b}\times \dfrac{d}{c}\]. Multiplying numerators and denominators, we get \[\dfrac{ad}{bc}\]. If the numerator and denominator have any common factors, we need to cancel them to get the simplest form of this expression.

Complete step by step solution:
We are asked to divide \[\dfrac{3}{4}\] by \[\dfrac{2}{5}\]. We already know how to divide two fractions \[\dfrac{a}{b}\And \dfrac{c}{d}\]. Here the values of a, b, c, and d are 3, 4, 2, and 5 respectively. Dividing these two fractions, we get
\[\Rightarrow \dfrac{\dfrac{3}{4}}{\dfrac{2}{5}}\]
Simplifying the above expression, we get
\[\Rightarrow \dfrac{3}{4}\times \dfrac{5}{2}\]
Multiplying 3 and 5 in the numerator we get 15, and multiplying 4 with 2 in the denominator we get 8. Thus, we get
\[\Rightarrow \dfrac{15}{8}\]
As 15 and 8 do not have any common factors, this expression can not be further simplified.
Hence, by dividing \[\dfrac{3}{4}\] by \[\dfrac{2}{5}\] we get \[\dfrac{15}{8}\].

Note: The above method can be remembered using a simple result which states that dividing two numbers is the same as multiplication of the first number and multiplicative inverse of the second. For the above example, we can use this result as follows:
The multiplicative inverse of the second number \[\dfrac{2}{5}\] is \[\dfrac{5}{2}\]. Thus, from the above result, multiplying the first number \[\dfrac{3}{4}\] with this inverse, we get \[\dfrac{3}{4}\times \dfrac{5}{2}=\dfrac{15}{8}\].
Thus, we get the same result from both methods.