Solve the proportion 35 over 28 equals x over 4. What is the value of x?

Apr 9, 2017

$x = 5$

Explanation:

$\frac{35}{28} = \frac{x}{4}$
This is a ratio statement. The most common way to solve this is to use cross multiplication. I'll show you how to solve it that way (it's just a shortcut), but first I'll go through it step-by-step

First, our goal is to get rid of the denominators.
$\cancel{28} \cdot \frac{35}{\cancel{28}} = \frac{x}{4} \cdot 28$
That's one denominatro cleared, now on to the next one:
$4 \cdot 35 = \frac{28 x}{\cancel{4}} \cdot \cancel{4}$
$4 \cdot 35 = 28 x$ or $140 = 28 x$

Now we need to isolate the $x$, so we just need to divide by $28$ on both sides
$\frac{140}{28} = \frac{\cancel{28} x}{\cancel{28}}$
That simplifies to $5 = x$

Now, to solve the same problem using cross multiplication, we begin with $\frac{35}{28} = \frac{x}{4}$. We just multiply the numerators ($35$ and $x$) by $4$ and $28$ respectively, and then we divide by $28$.

It looks like this:
$35 \cdot 4 = 28 \cdot x$
$\frac{35 \cdot 4}{28} = x$
$\frac{140}{28} = x$
$5 = x$

It just means skipping steps, but as long as you know what steps you're brushing over, you should be fine.

Apr 9, 2017

See the entire solution process below:

Explanation:

First, we can rewrite this written expression as:

$\frac{35}{28} = \frac{x}{4}$

Now, multiply each side of the equation by $\textcolor{red}{4}$ to solve for $x$ while keeping the equation balanced:

$\textcolor{red}{4} \times \frac{35}{28} = \textcolor{red}{4} \times \frac{x}{4}$

$\cancel{\textcolor{red}{4}} \times \frac{35}{\textcolor{red}{\cancel{\textcolor{b l a c k}{28}}} 7} = \cancel{\textcolor{red}{4}} \times \frac{x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}$

$\frac{35}{7} = x$

$5 = x$

$x = 5$