Question

Which of the following could be a real world description of four times over seven?

1) Four apples divided into seven equal parts
2) Four groups of seven students each
3) Four times the number seven
4) Four times the reciprocal of seven

Answer 1

The correct real-world description of 'four times over seven' is option 4: Four times the reciprocal of seven. This means multiplying four by 1/7, the reciprocal of seven, which aligns with the mathematical relationship between multiplication and reciprocals.

Step-by-step explanation:

The expression four times over seven can be understood in a real-world context using the concept of reciprocals and multiplication. To find a real-world description that matches this expression, let's consider the provided options:

• Four apples divided into seven equal parts - This suggests taking four whole items and dividing them, which isn't a match for the original phrase.
• Four groups of seven students each - This implies multiplication, but not of a reciprocal. It represents 4 times 7, rather than 4 times 1/7.
• Four times the number seven - Similar to the above, it's a straightforward multiplication, not involving a reciprocal
• Four times the reciprocal of seven - This is the correct real-world description of the original phrase since the reciprocal of seven is 1/7, and multiplying that by four gives four sevenths.

To illustrate, dividing by 8 is the same as multiplying by its reciprocal 1/8. Similarly, multiplying by 1/2 is the same as dividing by 2. This demonstrates how multiplication and division are related, and in this case, four times over seven means multiplying four by the reciprocal of seven.