Question

Simplify the following $\dfrac{4}{9}\div \dfrac{-5}{12}$.

Answer 1

Hint: To solve such types of questions we need to know the basic maths to solve i.e. addition, subtraction, multiplication, and division. Addition and subtraction are easy as they are simple $a+b$and$a-b$. But while multiplication or division we had to be more focused. Here to divide the equation you simply go with basics i.e. $a\div b$, be easily solved if we write it as $\dfrac{a}{b}$ and cut the numerator values by the number of times it will occur through the denominator.

Complete step by step solution:
As in our question, we had $\dfrac{4}{9}\div \dfrac{-5}{12}$
 so as from the hint assume $\dfrac{4}{9}=a$ and$\dfrac{-5}{12}=b$. So according to hint, we have to write it in form of$\dfrac{a}{b}$, so will get$\dfrac{\dfrac{4}{9}}{\dfrac{-5}{12}}$.
Now to deal with the type of presentation follow the rule which is of type: $\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}$ so we will simplify it as$\dfrac{a\times d}{b\times c}$. This means we had taken the lowermost number i.e. ‘d’ to the upper one i.e. ‘a’ and multiplied, similarly we had taken the second number i.e. ‘b’ and multiplied it with the third number i.e. ‘c’. If it will be of form $\dfrac{\dfrac{a}{b}}{c}$ then we will assume that below ‘c’ we had 1 and solve it according to the upper one which will give us$\dfrac{a\times 1}{b\times c}$.
So from the above explanation $\dfrac{\dfrac{4}{9}}{\dfrac{-5}{12}}$ can be written as$\dfrac{4\times 12}{9\times (-5)}$. Now we can solve them easily. First, solve the upper and lower value separately, i.e. $4\times 12$ and$9\times (-5)$.
Since we know that $4\times 12=48$and$9\times (-5)=-45$. Now put the value which we got i.e. $\dfrac{4\times 12}{9\times (-5)}=\dfrac{48}{-45}$which can be further written as$\dfrac{4\times 12}{9\times (-5)}=-\dfrac{48}{45}$.
Now to solve it further or to simply it these numerator and denominator values we get should have some common factor. Through which we can reduce these values. So here both 48 and -45 consist of common factor 3. So divide both by 3. So we will get $\dfrac{48}{3}=16$and$\dfrac{45}{3}=15$. So we to $-\dfrac{48}{45}=-\dfrac{16}{15}$. Since now 16 and 15 do not have any common factor so it will be the final answer.
So $-\dfrac{16}{15}$is the answer.

Note: To solve such simple solutions you need to know the mathematics table, at least up to 20. So that you can easily multiply and divide the numbers. Moreover, top simplifies the $\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}$ type, note that it consists of four numbers, and if you want to do it of three numbers please refer above explanation.