Question

1. \\(\frac{9}{10} = \frac{9x}{70}\\)

Explanation:

Step1: Cross - multiply the equation

To solve the proportion $\frac{9}{10}=\frac{9x}{70}$, we use the cross - multiplication property of proportions. If $\frac{a}{b}=\frac{c}{d}$, then $a\times d = b\times c$. So we have $9\times70 = 10\times9x$.
$$9\times70=10\times9x$$

Step2: Simplify both sides

First, calculate the left - hand side: $9\times70 = 630$. Then, calculate the right - hand side: $10\times9x=90x$. So the equation becomes $630 = 90x$.

Step3: Solve for x

Divide both sides of the equation $630 = 90x$ by 90. $\frac{630}{90}=x$.
$$x=\frac{630}{90}$$
Simplify $\frac{630}{90}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 90. $\frac{630\div90}{90\div90}=7$. So $x = 7$.

Answer:

$x = 7$