How to Use the Cross Product Property to Solve Equations Involving Fractions

cross products property

The cross product property, also known as the cross product rule or cross multiplication, is a property used when solving equations involving fractions

The cross product property, also known as the cross product rule or cross multiplication, is a property used when solving equations involving fractions. It is applicable when you have two fractions set equal to each other and you want to eliminate the fractions by multiplying both sides of the equation by the product of the denominators.

Let’s say you have the equation:

(a/b) = (c/d)

To eliminate the fractions, you can use the cross product property. It states that you can multiply both sides of the equation by the product of the denominators (b * d) without changing the equality. This will result in:

(a/b) * (b * d) = (c/d) * (b * d)

Simplifying both sides of the equation gives:

(a * d) = (c * b)

So, the cross product property allows you to multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction, and then set the two products equal to each other.

It is important to note that the cross product property is only applicable when both fractions are set equal to each other. It is used to eliminate the fractions and solve for the value of the variable in the equation.

Here is an example to illustrate the cross product property:

Solve for x:

(3/4) = (5/8) * x

To eliminate the fraction (5/8), we use the cross product property:

(3/4) * (8) = (5/8) * (8) * x

Simplifying both sides gives:

6 = 5x

Now, we can solve for x by dividing both sides of the equation by 5:

6 / 5 = (5x) / 5

x = 6/5

So, using the cross product property, we eliminated the fraction and solved for the value of x in the equation.

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