Question

Помогите пожалуйста сравнить дроби 7/9 и 14/18, 39/40 и 40/41 подробно

Answer 1

Пошаговое объяснение:

7/9 и 14/18

Для того чтобы сравнить эти дроби, приведу их к общему знаменателю. Для этого 7/9 и числитель , и знаменатель домножу на 2. Получится дробь 14/18.

Очевидно, что 14/18 = 14/18, поэтому 7/9=14/18

39/40 и 40/41

Домножу левую дробь(39/40) на 41, а правую(40/41) на 40.

Получаю :

1599/1640 и 1600/1640

Очевидно, что 1599/1640 < 1600/1640. Поэтому и 39/40 < 40/41

Answer 2

Comparing Fractions 7/9 and 14/18

To compare the fractions 7/9 and 14/18, we can simplify both fractions to their simplest form and then compare them.

Let's start with the fraction 7/9. To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator, which is the largest number that divides both numbers evenly. In this case, the GCD of 7 and 9 is 1. By dividing both the numerator and denominator by 1, we get the simplified fraction:

7/9 = 7 ÷ 1 / 9 ÷ 1 = 7/9

Now let's simplify the fraction 14/18. The GCD of 14 and 18 is 2. By dividing both the numerator and denominator by 2, we get the simplified fraction:

14/18 = 14 ÷ 2 / 18 ÷ 2 = 7/9

As we can see, both fractions simplify to the same value of 7/9. Therefore, the fractions 7/9 and 14/18 are equivalent.

Comparing Fractions 39/40 and 40/41

To compare the fractions 39/40 and 40/41, we can again simplify both fractions to their simplest form and then compare them.

Starting with the fraction 39/40, we can see that the numerator and denominator do not have a common factor other than 1. Therefore, the fraction 39/40 is already in its simplest form.

Now let's simplify the fraction 40/41. Similar to the previous fraction, the numerator and denominator do not have a common factor other than 1. Hence, the fraction 40/41 is also in its simplest form.

Since both fractions are already in their simplest form, we can compare them directly. The fraction 39/40 is less than the fraction 40/41 because the numerator (39) is smaller than the numerator (40), and the denominator (40) is larger than the denominator (41).

Therefore, we can conclude that:

39/40 < 40/41

I hope this helps! Let me know if you have any further questions.