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Cross-multiplication is a powerful technique that helps to solve proportions easily. When you have a proportion, say \( \frac{a}{b} = \frac{c}{d} \), cross-multiplication means you multiply the numerator of one fraction with the denominator of the other. This results in the equation \( a \times d = b \times c \). Using cross-multiplication simplifies the process by converting a proportion into a simple algebraic equation.

Here's why this is useful:

• It eliminates the fractions, making the calculation straightforward.
• Cross-multiplication ensures that the original ratios remain balanced.

In our exercise, we set up the cross-multiplication as \( 15 \times 128 = x \times 16 \). This shows that finding \( x \) involves straightforward arithmetic, making it easier to solve.

Understanding equivalent fractions is fundamental to solving proportions. Equivalent fractions represent the same part of a whole or the same ratio, even though they might look different. For example, \( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \) and \( \frac{3}{6} \).

In the exercise given:

• The fraction \( \frac{15}{16} \) needs to equal \( \frac{x}{128} \).
• Finding the correct \( x \) is all about ensuring these fractions are equivalent.

By preserving the equality after adjusting one side, we're making sure that both sides still represent the same relationship. In practice, identifying or creating equivalent fractions often involves multiplying or dividing both the numerator and denominator by the same number. In this exercise, utilizing cross-multiplication helps ascertain the right value for \( x \) that maintains this equivalency.

Solving proportions is about determining the missing value in a set of equivalent fractions, ensuring the balance of the two ratios. The key steps include setting up the equation using the known values, applying cross-multiplication, and then simplifying to find the unknown.

For our problem, the process was:

• Identify the proportion: \( \frac{15}{16} = \frac{x}{128} \).
• Use cross-multiplication to form the equation: \( 15 \times 128 = x \times 16 \).
• Solve the equation: Calculate \( 15 \times 128 = 1920 \) and then divide by 16 to get \( x = 120 \).

Solving proportions often involves simple arithmetic and algebra. Thus, it is not only an essential math skill but also very handy in various real-life situations where relationships between quantities need to be determined or maintained.