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Cross-multiplication is a reliable method to check if two ratios form a proportion. In simple terms, it involves multiplying the numerator of one fraction by the denominator of the other fraction. Then, you multiply the numerator of the second fraction by the denominator of the first one. These two products help determine the relationship between the two fractions.
For the problem given, you'll perform the multiplications as follows: multiply 13.23 by 11.35, and 39.96 by 3.45. These operations will give you the products to compare.

• Formula for cross-multiplication: Given two fractions \(\frac{a}{b} = \frac{c}{d}\), check if \(a \times d = b \times c\).
• Apply to the given exercise: Check if \(13.23 \times 11.35 = 39.96 \times 3.45\).

Using cross-multiplication helps you quickly ascertain if the two fractions are proportional without needing to find a common denominator.

Understanding the roles of the numerator and denominator is crucial in the context of fractions and proportions. The numerator is the top number in a fraction, representing how many parts of the whole or collection are being considered. On the other hand, the denominator is the bottom number, showing how many total equal parts the whole is divided into.
In the expression \(\frac{13.23}{3.45} = \frac{39.96}{11.35}\):ul>

The first fraction has a numerator of 13.23 and a denominator of 3.45.

The second fraction features a numerator of 39.96 and a denominator of 11.35.

Knowing these positions helps set up comparisons and operations like cross-multiplication. This organization allows us to systematically perform multiplication and comparisons to determine proportionality.

Looking at the results from cross-multiplication is vital to confirm whether the two fractions form a true proportion. After obtaining the two products, the key step is to check if they are equal. If they are, the two fractions are proportional, which means they have the same size relationship or ratio. If not, they aren't a proportion.
For instance, after performing the cross-multiplication on both fractions in the given exercise, you get two numerical results. Compare these two numbers:

• If \(13.23 \times 11.35 = 39.96 \times 3.45\), then the fractions are proportional.
• If they are not equal, the fractions are not proportional.

This step ensures you're comparing corresponding values correctly to establish proportional relationships. Understanding the comparison of products is important, as it concludes the evaluation of proportional relationships in fractions.