Chapter 7.1, Problem 45HP

To determine

Calculate percent between $\frac{3}{4}$ and $\frac{7}{9}$

Answer to Problem 45HP

Percent between $\frac{3}{4}$ and $\frac{7}{9}$ is $76.35\%$

Explanation of Solution

Given:

  $\frac{3}{4}$ and $\frac{7}{9}$

Calculations:

Here, we have to calculate percent between two fractions.

Firstly we have to find percent of each given fraction

  $\frac{3}{4}=0.75=0.75\times 100=75\%$

  $\frac{7}{9}=0.777=0.777\times 100=77.7\%$

Now to calculate percent between above obtained percent, we need to add both percents and then divide them by 2.

  $\frac{75\%+77.7\%}{2}=\frac{152.7}{2}=76.35\%=0.7635$

Another method to find percent between fraction is that, denominator should be same.

  $\begin{array}{l}\left(\frac{3}{4}\times \frac{9}{9}\right)+\left(\frac{7}{9}\times \frac{4}{4}\right)=\frac{27}{36}+\frac{28}{36}\\ =\frac{27+28}{36}\\ =\frac{55}{36}\end{array}$

Now we have to divide this fraction by 2, we get

  $\frac{55}{36}÷2=\frac{55}{36}\times \frac{1}{2}=\frac{55}{72}=0.7635=76.35\%$

Conclusion:

Therefore, we are able to calculate percent between given two fractions by simple mathematical methods.