Question

Evaluate$\frac{a-b}{c-d}$ for each set of values.

$a=7,b=6,c=9,d=5$

Short answer

The value of expression is $\frac{1}{2}$.

Step-by-step solution

Step 1. State the 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 similarsign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Step 2. Substitute the values.

In order to calculate $\frac{a-b}{c-d}$, substitute 7 for a, 6 for b, 9 for c and 5 for d.

$\frac{a-b}{c-d}=\frac{7-6}{9-5}$

Step 3. Simplify the expression.

Evaluate the expression in numerator and denominator.

$\begin{array}{c}\frac{a-b}{c-d}=\frac{7-6}{9-5}\\ =\frac{1}{4}\end{array}$

Thus, the solution of the expression is $\frac{1}{4}$.