Question

What is \[\dfrac{7}{8}\] divided by \[\dfrac{2}{3}\]?

Answer 1

Hint: In this question, provided with two numbers. And we have to calculate the exact value by dividing one number with the other. Take the number with whom we are dividing the other number. Let choose the number \[\dfrac{7}{8}\] as dividend and taken it as numerator and \[\dfrac{2}{3}\] as divisor and take it as denominator and further simplify by using fraction division operation to get the required value.

Complete step-by-step answer:
The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication.
Consider, the given question
We have to find the exact value when \[\dfrac{7}{8}\] divided by \[\dfrac{2}{3}\].
Here we consider, \[\dfrac{7}{8}\] as dividend and take it as in the numerator and
\[\dfrac{2}{3}\] as a divisor takes it as in the denominator.
We can represent the given question in division form as:
\[ \Rightarrow \,\,\dfrac{{\left( {\dfrac{7}{8}} \right)}}{{\left( {\dfrac{2}{3}} \right)}}\]
To solve this, we have to take denominator to numerator, then
\[ \Rightarrow \,\,\dfrac{7}{8} \times \dfrac{3}{2}\]
Now, it’s in the form of fraction multiplication, this can be solved by Multiplying the numerator with the numerator and Multiplying the denominator with the denominator.
Then,
\[ \Rightarrow \dfrac{{21}}{{16}}\]
This cannot be simplified further without using a calculator, when using a calculator we get the exact value i.e.,
 \[ \Rightarrow \dfrac{{21}}{{16}} \simeq 1.3125\]
Hence, it’s a required answer.

Note: In this question, \[\dfrac{7}{8}\] is the dividend \[\dfrac{2}{3}\] is the divisor and dividing these we got \[\dfrac{{21}}{{16}}\] as quotient and \[0\] is our remainder. We can also check our answer by using the dividend divisor remainder method. Where we can use the formula known as the remainder formula:
Dividend \[ \div \] divisor \[ = \] quotient \[ + \] remainder \[ \div \] divisor
Or can be written as
Dividend \[ = \] Quotient \[ \times \] divisor \[ + \] remainder.
\[\dfrac{7}{8} = \dfrac{{21}}{{16}} \times \dfrac{2}{3} + 0\]
\[\dfrac{7}{8} = \dfrac{{42}}{{48}}\]
Divide both numerator and denominator of RHS by 6, then
On simplification, we get
\[\dfrac{7}{8} = \dfrac{7}{8}\]
Which verified our answer.