Comparing Fractions
To compare two fractions we first need to make same denominators using equivalence of fractions. After this denominators are already equal, so we compare numerators just like we compared integers.
If we compare mixed numbers then we compare integer parts. If integer parts are equal then we need to compare fractional parts.
Example 1. Compare and .
Denominators are already equal, so we compare numerators: since then .
Answer: .
Now, let's do an example with unlike denominators.
Example 2. Compare and .
Make same denominators: and .
So, we compare and .
Denominators are equal, so we compare numerators: since then .
Answer: .
Next example.
Example 3. Compare and .
We don't need to make denominators equal, because negative number is always less than positive.
Answer: .
Now, do a couple of exercises.
Exercise 1. Compare and .
Answer: .
Next exercise.
Exercise 2. Compare and .
Answer: . Hint: compare integer parts: .
Next exercise.
Exercise 3. Compare and .
Ignore minuses.
Integer parts are equal, so we compare fractional parts: and .
Since then .
Add minus sign and change direction of inequality: .
Answer: .
Next exercise.
Exercise 4. Compare and .
Notice that is proper fraction so it can be treated as mixed number with integer part 0.
Now, compare integer parts: since then .
Answer: .
Next exercise.
Exercise 5. Compare and .
First fraction is improper, so this is not a mixed number.
We have two ways: either to convert improper fraction to mixed number or convert mixed number to improper fraction.
Let's choose first way: .
Now, we compare and .
Since then .
Answer: .