Question

Find a counter example to show that the following statement is false:

Answer 1

Answer:

Option D. is the answer.

Step-by-step explanation:

The given statement is $\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$

Now we have to find a counter example from the given options that the statement is False.

A. a = 3, b = 5, c = -3, d = 5

$\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$=$\frac{3}{5}+\frac{-3}{5}=\frac{3-3}{5+5}$

0 = 0

So the given statement is true.

B. a = 0, b = 4, c = 0, d= 9

$\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$

0 + 0 = 0

So for this example the given statement is true.

C. a = -2, b = 1, c = 2, d = 1

$\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$

$\frac{-2}{1}+\frac{2}{1}=\frac{-2+2}{1+1}$

0 = 0

Statement is true for these values.

D. a = 1, b = 2, c = 1, d = 2

$\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$

$\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2+2}$

$1=\frac{1}{2}$

Therefore, for these values of a, b, c and d, the given statement is False.

Option D. is the answer.