|Method II. Using the arithmetical process
- The denominators are same:
If the denominators are same, the fraction with the smaller numerator is less than the other.
Example: Compare -3/8 and -7/8?
In the given rational numbers the denominators are same, so we compare the numerators.
-7 is less than -3, therefore, -7/8 < -3/8
- The numerators are same:
If the numerators are same, the fraction with the smaller denominator is greater than the other.
Example: Compare 1/2 and 1/3?
In the given rational numbers, the numerators are same, so we compare the denominators.
i.e., 2 is less than 3, therefore, 1/2 > 1/3
- The numerators and denominators are different:
If the denominators of two fractions are not same, we should change them into fractions having the same denominators.
Example: Compare 3/5 and 4/7?
In the given rational numbers, the denominators are not same, so we change them to like denominators.
3/5 = 3/5 x 7/7 = 3x7/5x7 = 21/35.
4/7 = 4/5 x 5/5 = 4x5/7x5 = 20/35.
Now the denominators are same and 20 is less than 21.
Therefore, 20/35 < 21/35.
i.e., 4/7 < 3/5.
Directions: Compare the given rational numbers using arithmetical process, and use the sign "<" or ">" to answer. Also write at least 10 examples of your own.