How do you find a number that is between 7/11 and 7/10?

Hint: This question is from the topic of pre-algebra. In this question, we will find the number between the given numbers. In solving this question, we will first find the lowest common factor (that means L.C.M.) of 11 and 10. After that, we will make both the denominators equal to L.C.M. of 11 and 10. After that, we will see the numbers that come in between \[\dfrac{7}{11}\] and \[\dfrac{7}{10}\].

Complete step by step solution:
Let us solve this question.
In this question, we have asked to find a number between \[\dfrac{7}{11}\] and \[\dfrac{7}{10}\].
So, let us first find out the L.C.M. or lowest common factor of 11 and 10.
\[\begin{align}
  & 2\left| \!{\underline {\,
  11,10 \,}} \right. \\
 & 5\left| \!{\underline {\,
  11,5 \,}} \right. \\
 & 11\left| \!{\underline {\,
  11,1 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,1 \,}} \right. \\
\end{align}\]
Therefore, we can say that the L.C.M. of 11 and 10 is
\[L.C.M.\left( 11,10 \right)=2\times 5\times 11\times 1=110\]
Now, we will make the denominator of the numbers \[\dfrac{7}{11}\] and \[\dfrac{7}{10}\] equal to 110.
So, we can write the number \[\dfrac{7}{11}\] as
\[\dfrac{7}{11}=\dfrac{7\times 10}{11\times 10}=\dfrac{70}{110}\]
Similarly, we can write the number \[\dfrac{7}{10}\] as
\[\dfrac{7}{10}=\dfrac{7\times 11}{10\times 11}=\dfrac{77}{110}\]
Now, we have the numbers \[\dfrac{7}{11}\] and \[\dfrac{7}{10}\] as \[\dfrac{70}{110}\] and \[\dfrac{77}{110}\].
Now, let us find the numbers between the numbers \[\dfrac{70}{110}\] and \[\dfrac{77}{110}\].
As there will be too many numbers between the numbers \[\dfrac{70}{110}\] and \[\dfrac{77}{110}\], so let us write the numbers from the following:
\[\dfrac{71}{110}\], \[\dfrac{72}{110}\], \[\dfrac{73}{110}\], \[\dfrac{74}{110}\], \[\dfrac{75}{110}\], and \[\dfrac{76}{110}\]
So, we have got the numbers between \[\dfrac{70}{110}\] and \[\dfrac{77}{110}\] or we can say the numbers between \[\dfrac{7}{11}\] and \[\dfrac{7}{10}\]. We can take any of the numbers between \[\dfrac{7}{11}\] and \[\dfrac{7}{10}\].
We can say that a number between \[\dfrac{7}{11}\] and \[\dfrac{7}{10}\] is \[\dfrac{75}{110}\].

Note: We should have a better knowledge in the topic of pre-algebra to solve this type of questions easily. Remember that whenever we have to find the numbers between any two numbers, then we will first find the L.C.M. of denominators and make the denominators equal by using the L.C.M.