Final answer:
Option A (1/2 ÷ 1/4) equals 2, and Option C (2/5 ÷ 1/10) equals 4, which can easily be represented using a number line. These equations show simple cases where the divisor is a unit fraction, making their division intuitive and straightforward to visualize on a number line.
Step-by-step explanation:
Dividing a fraction by a fraction can indeed be represented using a number line. Let's look at the provided options:
- Option A: 1/2 ÷ 1/4 = 2. Dividing one-half by one-fourth is equivalent to finding how many one-fourths fit into one-half. On the number line, if you take one-half and divide it into two equal parts of one-fourth each, you see that it takes two sections of one-fourth to make up one-half. Therefore, 1/2 ÷ 1/4 equals 2.
- Option B: 3/4 ÷ 2/3 - This division is more complex to represent on a number line and would require subdividing into twelve parts since 12 is the least common multiple of 4 and 3.
- Option C: 2/5 ÷ 1/10 = 4. To visualize this on the number line, divide the line into ten parts to represent tenths, and see that two-fifths is the same as four-tenths. Therefore, four sections of one-tenth each fit into two-fifths, meaning 2/5 ÷ 1/10 equals 4.
- Option D: 5/8 ÷ 4/7 - Here, representation on a number line would involve subdividing the line into 56 parts since 56 is the least common multiple of 8 and 7, which is not as straightforward to visualize.
Based on this explanation, option A and option C can be represented using a number line in a simple and intuitive manner where multiplying by is the same as dividing and vice versa. Option A (1/2 ÷ 1/4) and Option C (2/5 ÷ 1/10) allow for a clear representation on a number line because the divisions equal whole numbers. In other words, these divisions result in integers, which can easily be plotted on a number line without further subdivision. Remember that when dealing with divisions like these, the divisor fraction is converted to its reciprocal and then that reciprocal is multiplied by the initial fraction. Therefore, dividing by a fraction is the same as multiplying by its reciprocal.