Chapter 6, Problem 57SGR

To determine

the solution of the proportion $\frac{7}{4}=\frac{f-4}{8}$ .

Answer to Problem 57SGR

  $f=18$

Explanation of Solution

Given:

The proportion, $\frac{7}{4}=\frac{f-4}{8}$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $\frac{7}{4}=\frac{f-4}{8}$ for the variable, isolate the variable term f on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate f on both side, first multiply both sides by 8 and then add both sides by 4 and then simplify further as shown below,

  $\begin{array}{c}\frac{7}{4}=\frac{f-4}{8}\\ \frac{7}{4}\cdot 8=\frac{f-4}{8}\cdot 8\\ \frac{56}{4}=f-4\\ 14=f-4\\ 14+4=f-4+4\\ 18=f\\ \Rightarrow f=18\end{array}$

Thus, the solution of the proportion is $f=18$ .