Question

Rewrite the equation $\frac {5}{b}=10$ as two equations joined by "and."
$\frac {5}{b}=10$ and $b\neq $ $\square $

Answer 1

To rewrite the equation \(\frac{5}{b} = 10\) as two equations joined by "and," we first solve for \(b\).

Starting with the equation:
\[
\frac{5}{b} = 10
\]

We can multiply both sides by \(b\) (noting that \(b \neq 0\)):
\[
5 = 10b
\]

Next, we divide both sides by 10:
\[
b = \frac{5}{10} = \frac{1}{2}
\]

Now we have:
1. \(b = \frac{1}{2}\)
2. \(b \neq 0\) (since we cannot divide by zero in the original equation)

Thus, we can rewrite the equation as:
\[
b = \frac{1}{2} \quad \text{and} \quad b \neq 0
\]

Inserting the value into the blank, we get:
\[
\frac{5}{b} = 10 \quad \text{and} \quad b \neq 0
\]

So, the final answer is:
\[
\frac{5}{b} = 10 \quad \text{and} \quad b \neq 0
\]