Complete the hypothesis about the product of two rational numbers.
Select the correct answer from each drop-down menu.
The product of two rational numbers is __________ equivalent to the ratio of __________ number because multiplying two rational numbers is __________ which is __________ number.
Answer (2)
The product of two rational numbers is equivalent to the ratio of two integers.
Multiplying two rational numbers involves multiplying their numerators and denominators.
The result of multiplying two rational numbers is a rational number.
Therefore, the completed statement is: The product of two rational numbers is equivalent to the ratio of tw o in t e g ers because multiplying two rational numbers is m u lt i pl y in g t h e i r n u m er a t ors an dd e n o mina t ors , which is a r a t i o na l number.
Explanation
Problem Analysis We need to complete the statement about the product of two rational numbers. Let's analyze each part of the statement.
Understanding Rational Numbers The product of two rational numbers is always a rational number. A rational number can be expressed as a fraction q p , where p and q are integers and q = 0 . When we multiply two rational numbers, say b a and d c , we get b × d a × c . Since the product of two integers is also an integer, the resulting fraction is a ratio of two integers.
Completing the Statement Therefore, the product of two rational numbers is equivalent to the ratio of two integers because multiplying two rational numbers is multiplying their numerators and denominators, which is resulting in a rational number.
Final Answer The completed statement is: The product of two rational numbers is equivalent to the ratio of two integers because multiplying two rational numbers is multiplying their numerators and denominators , which is a rational number.
Examples
Understanding rational numbers is crucial in various real-life scenarios. For instance, when calculating proportions in recipes, determining percentage discounts while shopping, or dealing with financial ratios, we often encounter rational numbers. Knowing that the product of two rational numbers is always rational ensures that our calculations remain within the realm of rational values, maintaining accuracy and consistency in our results. This concept is fundamental in fields like cooking, finance, and engineering, where precise calculations involving fractions and ratios are essential for success.
The product of two rational numbers is equivalent to the ratio of two integers because multiplying their numerators and denominators results in a rational number.
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