Question

Найди среди чисел 1 1/7;3 1/2;7/9;7 1/2 взаимо обратные. Выпишите их и поясните свой выбор.

Answer 1

Finding the Reciprocals of the Given Numbers

To find the reciprocals of the numbers 1 1/7, 3 1/2, 7/9, and 7 1/2, we need to invert each of these numbers. The reciprocal of a number is obtained by dividing 1 by that number.

Let's calculate the reciprocals of the given numbers:

1. 1 1/7: - To find the reciprocal of 1 1/7, we divide 1 by 1 1/7. - The reciprocal of 1 1/7 is 7/8.

2. 3 1/2: - To find the reciprocal of 3 1/2, we divide 1 by 3 1/2. - The reciprocal of 3 1/2 is 2/7.

3. 7/9: - To find the reciprocal of 7/9, we divide 1 by 7/9. - The reciprocal of 7/9 is 9/7.

4. 7 1/2: - To find the reciprocal of 7 1/2, we divide 1 by 7 1/2. - The reciprocal of 7 1/2 is 2/15.

Explanation of the Choices

The reciprocals of the given numbers are as follows:

- Reciprocal of 1 1/7: 7/8 - Reciprocal of 3 1/2: 2/7 - Reciprocal of 7/9: 9/7 - Reciprocal of 7 1/2: 2/15

The choice of these reciprocals is based on the mathematical operation of inversion. When we find the reciprocal of a number, we essentially flip the numerator and denominator of the fraction or divide 1 by the given number. This is done to find the value that, when multiplied by the original number, gives a product of 1.

For example, the reciprocal of 1 1/7 is 7/8. If we multiply 1 1/7 by 7/8, the result is 1. Similarly, if we multiply 3 1/2 by 2/7, the result is 1. This holds true for the reciprocals of 7/9 and 7 1/2 as well.

In summary, the reciprocals of the given numbers are obtained by inverting the fractions or dividing 1 by the given numbers.