Is 5/7 greater than 10/3?

To compare two fractions, such as 5/7 and 10/3, there are two main common methods: the first one involves finding a common denominator, and the other one is to convert the fractions directly into decimal values.

1) Using the same denominator

  1. Multiply the numerator of the first fraction with the denominator of the second fraction: 5 × 3 = 15
  2. Multiply the numerator of the second fraction with the denominator of the first fraction 10 × 7 = 70
  3. Multiply the denominators of both fractions together: 7 × 3 = 21
  4. Rewrite both fractions with the new common denominator:
    • 5/7 = 15/21
    • 10/3 = 70/21

With a common denominator, the comparison becomes much simpler.

Since 15 is smaller than 70, we can conclude that 5/7 is less than 10/3.

2) Converting to decimal

We can also simply convert the fractions into decimal values:

  1. 5 divided by 7 is equal to 0.71428571428571
  2. 10 divided by 3 is equal to 3.3333333333333

Since 0.71428571428571 is smaller than 3.3333333333333, it means that 5/7 is less than 10/3.