Chapter 8.1, Problem 44IP

To determine

Explain how to use the Multiplication Property of Equality to solve $\frac{2}{5}y=6$ .

Answer to Problem 44IP

y = 15

Explanation of Solution

Given:

Explain how to use the Multiplication Property of Equality to solve $\frac{2}{5}y=6$ . Then explain how to solve the equation using the Division Property of Equality.

Concept Used:

Multiplication Property of Equality: For all real numbers a, b, c, if a = b, then $a·c=b·c$

Division Property of Equality: For all real numbers a, b, c, and c ? 0, if a = b, then $\frac{a}{c}=\frac{b}{c}$

When you divide or multiply both sides of an equation by the same quantity, you still have equality.

Calculation:

Required Equation: $\frac{2}{5}y=6$

As 5 is in the denominator, so multiply by 5 to both sides: $5·\frac{2}{5}y=5·6\Rightarrow 2y=30$

Now 2 is the coefficient of y, we need to isolate y only in the left side, so divide each side by 2.

  $2y=30\Rightarrow \frac{2y}{2}=\frac{30}{2}\Rightarrow y=15$

Thus, the solution of the equation $\frac{2}{5}y=6$ is y = 15