Questions: Evaluate the given expression for (w=A ; x=3, y=13, z=12) (fracxw+fracyz) (fracxw+fracyz=) , when (w=4, x=3, y=13, z=12)

Solution Steps

To evaluate the given expression \(\frac{x}{w}+\frac{y}{z}\) with the values \(w=4\), \(x=3\), \(y=13\), and \(z=12\), substitute the given values into the expression and perform the arithmetic operations to find the result.

We start with the expression

\[ \frac{x}{w} + \frac{y}{z} \]

and substitute the given values \(w = 4\), \(x = 3\), \(y = 13\), and \(z = 12\):

\[ \frac{3}{4} + \frac{13}{12} \]

To add the fractions, we need a common denominator. The least common multiple of \(4\) and \(12\) is \(12\). We rewrite \(\frac{3}{4}\) with a denominator of \(12\):

\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]

Now, we can rewrite the expression as:

\[ \frac{9}{12} + \frac{13}{12} \]

Now that both fractions have the same denominator, we can add them:

\[ \frac{9 + 13}{12} = \frac{22}{12} \]

We simplify \(\frac{22}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\):

\[ \frac{22 \div 2}{12 \div 2} = \frac{11}{6} \]

Final Answer