# Using the Multiplicative Inverse to Solve Equations

The multiplicative inverse sounds like a weird sci-fi concept, but it's really just multiplying a fraction by its reciprocal—otherwise known as the same fraction flipped upside down. It's like an roller coaster ride for fractions! Just make sure they don't eat too much cotton candy beforehand.

Basic Algebra | Basic Equations |

Functions | Inverse Functions |

Language | English Language |

### Transcript

down there...

If it weren't for all the hoarding.

If the tower of cans grows three-quarters of a foot each month, how many months will

it take for all those canned beets and carrots to reach the ceiling?

Here are your options: First, we need to write this out in an equation.

Let's see if we can find a piece of paper and pencil in all this junk.

Okay, so we'll describe this as...

Current height of the cans...

Plus growth rate...

Times number of months... for which we'll use M as the variable -- notice the clever

first letter thing there -

Equals height of the ceiling which is 20 feet. We're solving for number of months, so that

value is M

Here's our finished equation: First, we need to subtract eleven from each

side.

We know you wish you could subtract that eleven-foot-stack of canned peas from your life, but this is

just hypothetical. Sorry.

That leaves us with three-fourths X on the left and nine on the right.

In order to get rid of the fraction, we need to multiply each side by the inverse of the

fraction.

Inverse means to flip the fraction over, kind of like multiplying by its opposite.

Just like you want to live in a house that isn't filled with horded emergency supplies.DELETE

In this case, the multiplicative inverse would be four over three. So multiply both sides

by four over three. That cancels out the three-fourths on the

left, leaving us with X.

Multiply nine by four over three to get thirty-six over three.

Simplify that to get twelve. The answer is B, X equals twelve. So it looks

like you have a year before your basement is totally full.

Look at the bright side. If a disaster does wipe out your house, you can live in a can

fort. Food and shelter in one convenient place.

Plus, you now have the invaluable survival skill of Using Multiplicative Inverse to Solve

Equations.

We'll be at your place when disaster strikes.