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'Cross Multiplication' is a valuable tool when dealing with algebraic equations that involve fractions. It allows us to solve equations by eliminating the fractions, making the equations easier to work with. The idea with cross multiplication is simple: what you do is multiply the numerator of one fraction by the denominator of the other fraction across the equal sign.

Consider the equation: \[\frac{x}{-9.9} = \frac{-7.7}{23.1}\]To solve this, you multiply the numerator of the first fraction, \(x\), by the denominator of the second fraction, \(23.1\), and set it equal to the numerator of the second fraction, \(-7.7\), multiplied by the denominator of the first fraction, \(-9.9\).

• This results in: \(x \times 23.1 = -7.7 \times -9.9\)

From there, once cross multiplication is complete, you are left with a much simpler equation to solve.

When faced with an algebraic equation, the goal is often to find the value of the variable that satisfies the equation. In our exercise, we want to 'Solve for x'. After applying cross multiplication to:

• We have: \(x \times 23.1 = -7.7 \times -9.9\)

The next step is to isolate \(x\). To do this, perform the multiplication on the right side first:

• Calculate \(-7.7\times(-9.9)\), which will give you a positive number.

After the multiplication, you have:\[ x \times 23.1 = 76.23 \]

Then, simply divide both sides of the equation by \(23.1\) to solve for \(x\):

• \(x = \frac{76.23}{23.1}\)

This calculation will give you the specific value of \(x\). Finally, crunch the numbers to find that \(x \approx 3.3\).

In equations like the one we are solving, 'Negative Fractions' play a crucial role. It's essential to understand how to work with them, especially when both the numerator and denominator have negative signs.

Recognize that multiplying two negative numbers, as in our exercise with \(-7.7\) and \(-9.9\), results in a positive product. So, when you see a fraction where either the numerator or the denominator is negative, don't panic!

• Remember: \(-7.7\) divided by \(23.1\) yields a negative number.
• Multiplying the negative numbers in the cross multiplication step negates the negatives yielding positive values in those cases.

This concept is not only crucial for solving the equation effectively but also empowering you to handle any algebra problems involving negative numbers in fractions.