i'm in my geometry book and i don' get number 28. it says the quotient of two proper fractions is a proper fraction. i'm a post to find a counterexample.
I NEED HELP
Answered below for the jj post.
Sure! I can help you understand the problem and find a counterexample.
In this problem, you are given a statement about proper fractions and asked to find a counterexample. A proper fraction is a fraction where the numerator (top number) is smaller than the denominator (bottom number).
To demonstrate that the statement is false, you need to find an example where the quotient (result of division) of two proper fractions is not a proper fraction.
Let's go step by step to find a counterexample:
1. Start by understanding the given statement: "The quotient of two proper fractions is a proper fraction." This statement suggests that when you divide one proper fraction by another, the resulting fraction is also a proper fraction.
2. Recall that dividing fractions involves multiplying the first fraction by the reciprocal (flipped version) of the second fraction. So, you'll need to divide two proper fractions to find the quotient.
3. Choose two proper fractions. To ensure that the quotient is not a proper fraction, you can select fractions that result in a fraction with a numerator larger than the denominator.
For example, let's consider the fractions 2/3 and 3/4. Both of these fractions are proper fractions because their numerators are smaller than their denominators.
4. Calculate the quotient of the two fractions. Divide 2/3 by 3/4 by multiplying 2/3 with the reciprocal of 3/4, which is 4/3.
(2/3) ÷ (3/4) = (2/3) * (4/3) = (2 * 4) / (3 * 3) = 8 / 9.
The resulting fraction, 8/9, has a numerator (8) that is larger than the denominator (9). Therefore, it is not a proper fraction.
5. Conclusion: You have found a counterexample that disproves the given statement. The example of dividing 2/3 by 3/4 provides a quotient of 8/9, which is not a proper fraction.
I hope this explanation helps you understand the problem better and how to find a counterexample! Let me know if you need further assistance.
To find a counterexample for the statement "the quotient of two proper fractions is a proper fraction," you need to find two proper fractions whose quotient is not a proper fraction.
A proper fraction is a fraction where the numerator (top number) is smaller than the denominator (bottom number). For example, 3/4, 2/5, or 1/3 are all examples of proper fractions.
To find a counterexample, you can try different values for the two fractions. Let's start by using 2/3 and 3/4 as the two fractions:
1. Find the quotient by dividing the numerators and denominators separately:
(2/3) ÷ (3/4) = (2/3) × (4/3) = 8/9
In this case, the quotient 8/9 is still a proper fraction, which means it does not serve as a counterexample.
Let's try another set of fractions, such as 3/4 and 5/6:
2. Find the quotient again:
(3/4) ÷ (5/6) = (3/4) × (6/5) = 18/20
In this example, the quotient 18/20 is not a proper fraction since the numerator is not smaller than the denominator. Therefore, this serves as a counterexample to the statement mentioned in your geometry book.
Remember, when looking for a counterexample, you just need to find a single instance where the statement does not hold true.