Chapter 4.3, Problem 53E

(a)

To determine

To find evaluate the expression and then simplify.

Answer to Problem 53E

  $\frac{4}{9}$

Explanation of Solution

Given information: $\frac{8x^{2}y}{6x^2{y}^2}$

Formula Used: Factorisation

Calculation:

  $x=2$ and $y=3$

  $\frac{8x^{2}y}{6x^2{y}^2}=\frac{8\times 2\times 2\times 3}{6\times 2\times 2\times 3\times 3}$

  $\frac{8x^{2}y}{6x^2{y}^2}=\frac{4}{9}$

(b)

To determine

To simplify the expression and then evaluate.

Answer to Problem 53E

  $\frac{4}{9}$

Explanation of Solution

Given information: $\frac{8x^{2}y}{6x^2{y}^2}$

Formula Used: Factorisation

Calculation:

  $x=2$ and $y=3$

Simplest form of $\frac{8x^{2}y}{6x^2{y}^2}=\frac{4}{3y}$

  $\frac{4}{3y}=\frac{4}{3\times 3}$

  $\frac{4}{3y}=\frac{4}{9}$

(c)

To determine

To compare the result.

Answer to Problem 53E

Results from parts (a) and (b) are same.

Method (b) requires less work because it needs less calculation.

Explanation of Solution

Given information: $\frac{8x^{2}y}{6x^2{y}^2}$

Formula Used: Factorisation

Calculation:

Results from parts (a) and (b) are same.

Method (b) requires less work because it needs less calculation.

(d)

To determine

To compare the result.

Answer to Problem 53E

Results are same.

Explanation of Solution

Given information: $\frac{8x^{2}y}{6x^2{y}^2}$

Formula Used: Factorisation

Calculation:

  $x=3$ and $y=4$

  $\frac{8x^{2}y}{6x^2{y}^2}=\frac{8\times 3\times 3\times 4}{6\times 3\times 3\times 4\times 4}$

  $\frac{8x^{2}y}{6x^2{y}^2}=\frac{1}{3}$

Simplest form of $\frac{8x^{2}y}{6x^2{y}^2}=\frac{4}{3y}$

  $\frac{4}{3y}=\frac{4}{3\times 4}$

  $\frac{4}{3y}=\frac{1}{3}$

So, Results are same.