Explain why the product of 1/2 and 7/8 is less than 1/2.
The Correct Answer and Explanation is:
To find the product of 1/2 and 7/8, we multiply the two fractions:12×78=1×72×8=716\frac{1}{2} \times \frac{7}{8} = \frac{1 \times 7}{2 \times 8} = \frac{7}{16}21×87=2×81×7=167
Now we compare 7/16 to 1/2.
Since 1/2 is equal to 8/16, and 7/16 is one part less than 8/16, we know that:716<816=12\frac{7}{16} < \frac{8}{16} = \frac{1}{2}167<168=21
Explanation:
When we multiply a fraction by a number, we are essentially taking that fraction of the number. In this case, we are finding one-half of seven-eighths. This is another way of asking, “What is half of 7/8?” The answer is 7/16.
To understand why 7/16 is smaller than 1/2, think of a pizza. Suppose the whole pizza is cut into 16 equal slices. If you have 8 out of the 16 slices, you have exactly half of the pizza. But if you only have 7 out of the 16 slices, you have less than half. This illustrates that 7/16 is less than 1/2.
The more general idea is that when you multiply a positive fraction by a number less than 1, the result is always smaller than the number you started with. Here, we multiplied 7/8 by 1/2. Since 1/2 is less than 1, the result must be less than 7/8. Also, since 7/8 is greater than 1/2, any smaller portion of 7/8 (like half of it) will also be less than 1/2.
This shows how multiplying fractions works: the smaller the number you multiply by (as long as it’s positive and less than 1), the smaller the result. So, because we are multiplying 7/8 by 1/2, the product will always be less than 1/2, unless the other number is 1. In this case, the product is 7/16, which is clearly smaller than 1/2.
