Is 10/3 greater than 5/7?

To compare two fractions, such as 10/3 and 5/7, 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: 10 × 7 = 70
  2. Multiply the numerator of the second fraction with the denominator of the first fraction 5 × 3 = 15
  3. Multiply the denominators of both fractions together: 3 × 7 = 21
  4. Rewrite both fractions with the new common denominator:
    • 10/3 = 70/21
    • 5/7 = 15/21

With a common denominator, the comparison becomes much simpler.

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

2) Converting to decimal

We can also simply convert the fractions into decimal values:

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

Since 3.3333333333333 is larger than 0.71428571428571, it means that 10/3 is greater than 5/7.