Chapter 4, Problem 24CR

To determine

To write the fraction in simplest form $\frac{22m^{2}n}{11m{n}^2}$

Answer to Problem 24CR

  $\frac{2m}{n}$

Explanation of Solution

Given information:

Expression $\frac{22m^{2}n}{11m{n}^2}$

Formula Used: Quotient rule with same base and Negative Exponent Rule

Calculation:

The Quotient Rule with same base says that when the bases are same and in division, the exponent powers are subtracted. In the given expression, have m and n in both numerator & denominator. On applying the Quotient rule,have

  $=\frac{22}{11}\times \left(\frac{m^2}{m^1}\right)\left(\frac{n^1}{n^2}\right)$

22 & 11 will divide to give us 2.

On applying the rule, get-

  $=2\times \left(m^{2-1}\right)\left(n^{1-2}\right)$

Hence,

  $=2\times \left(m^1\right)\left(n^{-1}\right)$

now apply the negative exponent rule to make the exponent positive.

  $=\frac{2m}{n}$

Conclusion-

  $=\frac{2m}{n}$