In this video, we will be learning how to solve proportions using cross-multiplication. After you finish this lesson, view all of our Pre-Algebra lessons and practice problems.

For Example:

$\dfrac{3}{5}=\dfrac{x}{14}\leftarrow$ First we cross-multiply

$\dfrac{42}{5}=\dfrac{5x}{5}\leftarrow$ Then we divide by 5 to isolate x

$x=\dfrac{42}{5}$

## Examples of Solving Proportions

### Example 1

$\dfrac{4}{8}=\dfrac{x+1}{6}$

First, we have to cross-multiply.

$4 \times 6 = 24$ then $8 \times(x+1)$

Next, distribute $8$ to $(x+1)$

$24 = 8x+8$

Subtract $8$ from both sides

$24-8=8x+8-8$ $16=8x$

Divide $8$ from both sides to get $x$

Our final answer is $x=2$

### Example 2

$\dfrac{2x-8}{4}=\dfrac{2}{5}$

First, we have to cross-multiply.

$4 \times 2 = 8$ then $5 \times(2x-8)$

Next, distribute $5$ to $(2x-8)$

$10x-40=8$

Add $40$ from both sides

$10x-40+40=8+40$ $10x=48$

Divide $10$ from both sides to get $x$

Our final answer is $x=4.8$

## Video-Lesson Transcript

In this video, we will be learning how to solve proportions using cross-multiplication.

Ratio = Ratio

$\dfrac{1}{4} = \dfrac{2}{8}$

Or $\dfrac{3}{5} = \dfrac{9}{15}$

Solving Proportions comes in when there is an unknown.

Let’s say we have $\dfrac{3}{5} = \dfrac{x}{15}$

We have to cross-multiply.

$3 \times 15 = 45$ then $5 \times x = 5x$

We have $45 = 5x$

Then we get the value of $x = 9$

But what about it is not a perfect multiplier?

For example, $\dfrac{3}{5} = \dfrac{x}{14}$

In this case, we cross-multiply $3 \times 14 = 42$ then $x \times 5 = 5x$

So we have $x = \dfrac{42}{5}$

Here we have to $42\div {5}$

So $x = 8.4$

Here’s another example.

$\dfrac{2}{5} = \dfrac{x + 1}{9}$

Let’s cross-multiply, $2 \times 9 = 18$ then $5 (x + 1)$

We have to distribute $18 = 5x + 5$

And we’ll have $13 = 5x$

To get the value of $x$ we have to $13\div 5$

Our final answer is $x = 2.6$