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:

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

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

x=\frac{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

Learn How To Solve Proportions

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