If a/b= 3/4, will the value of a/b +x/x be less than, equal to, greater than 3/4? Justify your answers by a means other than plugging in values for x.



Answer :

Answer:not equal

Step-by-step explanation:Given the expression \(\frac{a}{b} + \frac{x}{x}\), we need to determine if it will be less than, equal to, or greater than \(\frac{3}{4}\) under the condition \(\frac{a}{b} = \frac{3}{4}\).

First, let's rewrite the expression:

\[

\frac{a}{b} + \frac{x}{x}

\]

Notice that \(\frac{x}{x}\) simplifies to 1, as any non-zero number divided by itself is 1. So, we can simplify the given expression to:

\[

\frac{a}{b} + 1

\]

We know from the problem statement that:

\[

\frac{a}{b} = \frac{3}{4}

\]

Substituting this value into the expression, we get:

\[

\frac{3}{4} + 1

\]

Next, let's add these fractions. To add the fraction \(\frac{3}{4}\) and 1, we convert 1 to a fraction with a denominator of 4:

\[

1 = \frac{4}{4}

\]

Now, we can add the fractions:

\[

\frac{3}{4} + \frac{4}{4} = \frac{3+4}{4} = \frac{7}{4}

\]

Thus, the value of the expression \(\frac{a}{b} + \frac{x}{x}\) is \(\frac{7}{4}\).

To determine how \(\frac{7}{4}\) compares to \(\frac{3}{4}\), we can observe that:

\[

\frac{7}{4} > \frac{3}{4}

\]

Therefore, the value of \(\frac{a}{b} + \frac{x}{x}\) is greater than \(\frac{3}{4}\).

In conclusion, \(\frac{a}{b} + \frac{x}{x}\) will be greater than \(\frac{3}{4}\) given that \(\frac{a}{b} = \frac{3}{4}\).