Question

Determine if the proportio (3)/(5)=(6)/(10) Proportion is not true

Answer 1

The cross-products are equal. Cross-multiplying yields (30 = 30), confirming the proportionality of the two ratios. Therefore, the statement is valid. Thus The given proportion (3)/(5) = (6)/(10) is true.

Step-by-step explanation:

Proportions compare the relationship between two sets of numbers. In this case, we have (3)/(5) on one side and (6)/(10) on the other side. To determine if the proportion is true, we can cross-multiply and check if the two products are equal.

Let's cross-multiply:

`\[ (3 * 10) \ and \ (5 * 6) \]`

[30 and 30]

Since the cross-products are equal, the given proportion is true. This means that the ratio of 3 to 5 is equivalent to the ratio of 6 to 10. In other words, the two fractions represent the same proportional relationship, and the statement (3)/(5) = (6)/(10) holds.

Understanding proportions is essential in various mathematical contexts, such as scaling and solving problems involving ratios. In this case, the equality of the cross-products confirms that the given ratios are proportional, reinforcing the idea that the two fractions express the same relative size or magnitude relationship. Therefore, the proportion (3)/(5) = (6)/(10) is valid.