Chapter 4, Problem 11CT

To determine

To write the fraction in simplest form $\frac{8xy}{16y}$

Answer to Problem 11CT

  $\frac{x}{2}$

Explanation of Solution

Given information:

Expression $\frac{8xy}{16y}$

Formula Used: Factorization & Quotient Exponent Rule & Zero Exponent Rule

Calculation:

To reduce the fraction to its simplest form, break down the numerator & denominator into its factors. So,

  $\frac{8xy}{16y}=\frac{2\times 2\times 2\times x\times y}{2\times 2\times 2\times 2\times y}$

As both numerator & denominator has $2\times 2\times 2$ common, so they cancel out.

Also, as per the quotient exponent rule, when bases are same in division, exponents are subtracted. So for y, subtract the exponent.

In the next step,

  $=\frac{x{y}^{1-1}}{2}$

This gives us-

  $=\frac{x{y}^0}{2}$

On applying the zero exponent rule, final answer is-

  $=\frac{x}{2}$

Conclusion-

  $=\frac{x}{2}$