Question

12/108 и 70/180, 14/35 и 20/45, 8/64 и 175/280, 14/21 и 36/96.

Answer 1

12/108>70/180,14/35<20/45,8/64<175/280,14/21<36/96

Answer 2

To compare fractions, we can simplify them by finding the greatest common divisor (GCD) of their numerators and denominators. Then, we can compare the simplified fractions.

Let's go through each pair of fractions:

1. 12/108 and 70/180:

   Simplifying the fractions:

   • The GCD of 12 and 108 is 12, so we can simplify 12/108 to 1/9.
   • The GCD of 70 and 180 is 10, so we can simplify 70/180 to 7/18.

   Comparing the simplified fractions: 1/9 and 7/18

   To compare fractions with different denominators, we can find a common denominator. In this case, the common denominator is 18. We can convert both fractions to have the same denominator:

   • 1/9 can be converted to 2/18 (multiplying numerator and denominator by 2).
   • 7/18 remains the same.

   Now we can compare them: 2/18 < 7/18

   Therefore, 1/9 < 7/18.

2. 14/35 and 20/45:

   Simplifying the fractions:

   • The GCD of 14 and 35 is 7, so we can simplify 14/35 to 2/5.
   • The GCD of 20 and 45 is 5, so we can simplify 20/45 to 4/9.

   Comparing the simplified fractions: 2/5 and 4/9

   To compare fractions with different denominators, we can find a common denominator. In this case, the common denominator is 45. We can convert both fractions to have the same denominator:

   • 2/5 can be converted to 18/45 (multiplying numerator and denominator by 9).
   • 4/9 can be converted to 20/45 (multiplying numerator and denominator by 5).

   Now we can compare them: 18/45 < 20/45

   Therefore, 2/5 < 4/9.

3. 8/64 and 175/280:

   Simplifying the fractions:

   • The GCD of 8 and 64 is 8, so we can simplify 8/64 to 1/8.
   • The GCD of 175 and 280 is 35, so we can simplify 175/280 to 5/8.

   Comparing the simplified fractions: 1/8 and 5/8

   Since both fractions have the same denominator, we can directly compare their numerators: 1/8 < 5/8

   Therefore, 1/8 < 5/8.

4. 14/21 and 36/96:

   Simplifying the fractions:

   • The GCD of 14 and 21 is 7, so we can simplify 14/21 to 2/3.
   • The GCD of 36 and 96 is 12, so we can simplify 36/96 to 3/8.

   Comparing the simplified fractions: 2/3 and 3/8

   To compare fractions with different denominators, we can find a common denominator. In this case, the common denominator is 24. We can convert both fractions to have the same denominator:

   • 2/3 can be converted to 16/24 (multiplying numerator and denominator by 8).
   • 3/8 can be converted to 9/24 (multiplying numerator and denominator by 3).