Chapter 4, Problem 13CST

To determine

To determine who read the greater fraction of a novel.

Answer to Problem 13CST

  $\frac{23}{42}<\frac{5}{7}$

Hence the fraction of novel read by my friend is greater.

Explanation of Solution

Given information:

Fraction of novel read by me $\frac{23}{42}$

Fraction of novel read by my friend $\frac{5}{7}$

Formula Used: Least Common Denominator

Calculation:

The first step here is to identify the Least Common Denominator for both fractions. So, break the denominators into its multiples-

  $\frac{23}{42}=\frac{23}{7\times 2\times 3}$

For the other fraction, it is-

  $\frac{5}{7}=\frac{5\times 1}{7\times 1}$

In the above fractions, it is clear that the LCD is 7.

In the second step, extract the LCD, and rewrite the fractions as-

  $\frac{23}{42}=\frac{1}{7}\times \frac{23}{2\times 3}$

And the other one as-

  $\frac{5}{7}=\frac{1}{7}\times \frac{5}{1}$

Now our fractions are reduced to

  $\frac{23}{6}$ and $\frac{5}{1}$

Make the denominators of both fractions same by multiplying each fractions denominator, with the numerator & denominator of the other fraction.

So for first fraction-

  $\frac{23}{6}\times \frac{1}{1}=\frac{23}{6}$

And for the second fraction

  $\frac{5}{1}\times \frac{6}{6}=\frac{30}{6}$

Now, both the fractions have same denominator 6.

  $\frac{23}{6}$ , $\frac{30}{6}$

Since 23 is less than 30, so the first fraction is less than the second one.

  $\frac{23}{42}<\frac{5}{7}$

Hence the fraction of novel read by my friend is greater.

Conclusion-

  $\frac{23}{42}<\frac{5}{7}$

Hence the fraction of novel read by my friend is greater.