What operation is crucial for solving proportions in Mathematics?

What operation is crucial for solving proportions in Mathematics?

• A. Addition
• B. Subtraction
• C. Cross-multiplication
• D. Division

Answer: (C)

Cross-multiplication is essential for solving proportions because it provides a straightforward method to find the unknown value in a ratio. When two fractions are set equal to each other, cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal to each other. This approach simplifies the process of solving for the unknown variable and helps maintain the equality of the proportions. For instance, if you have the proportion \( \frac{a}{b} = \frac{c}{d} \), cross-multiplying leads to the equation \( a \cdot d = b \cdot c \). This step effectively allows one to isolate the variable and is fundamental in proving that two ratios are equivalent, making it a crucial operation in the realm of mathematics dealing with proportions.

Cross-multiplication is essential for solving proportions because it provides a straightforward method to find the unknown value in a ratio. When two fractions are set equal to each other, cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal to each other. This approach simplifies the process of solving for the unknown variable and helps maintain the equality of the proportions.

For instance, if you have the proportion ( \frac{a}{b} = \frac{c}{d} ), cross-multiplying leads to the equation ( a \cdot d = b \cdot c ). This step effectively allows one to isolate the variable and is fundamental in proving that two ratios are equivalent, making it a crucial operation in the realm of mathematics dealing with proportions.