In this video we will be looking at how to solve equations which involve multiplying by a fraction, using the Multiplicative Inverse Property.

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#### One-Step Equations: Multiplication Problems with Fractions

We have looked at multiplying and dividing one-step equations with integers,

Now lets see what happens when fractions are involved.

Lets start by looking at the problem: $\frac{-5x}{7}=35$

In this problem we are dividing by $7$, so we can get rid of that by multiplying each side by $7$, since as long as we do the same thing to both sides of the equation the equation will remain equal.

$7*\frac{-5x}{7}=35*7$

Giving us $-5x =245$

Now we can divide each side of the equation by $-5$

Leaving us with $x = -45$

Or we could solve the problem in one step. Just like before we will be using the multiplicative inverse property: which says that any number times its reciprocal equals 1.

The multiplicative inverse of $\frac{-5}{7}$ is $\frac{7x}{-5}$

So if we multiply both sides of the equation by $\frac{7x}{-5}$ on the left we apply the multiplicative inverse property and get 1x and on the left hand side of the equation we can simplify the problem before multiplying and we would get

So $x = -45$

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