Concept

Proper fraction:

A fraction in which the numerator is less than the denominator.

Improper fraction:

A fraction in which the numerator is greater than the denominator.

Mixed number:

A whole number and a proper fraction.

Rule

When comparing fractions:

1. Change both fractions, so they have like denominators.
2. The fraction that is larger will have the greatest numerator.

When comparing fractions:

1. Change mixed numbers into improper fractions.
2. Change fractions, so they have like denominators. 
3. The number that is larger will have the greatest numerator.

Example

Compare.

Solution

When comparing mixed numbers, and improper fractions:
Change both numbers into improper fractions.

386 is already an improper fraction.

To change 678 into an improper fraction, first multiply the whole number by the denominator.

6 × 8 = 48

Next, add this to the numerator.

48 + 7 = 55

Last, 55 becomes the new numerator. The denominator stays the same. 558

Change one or both fractions to a common denominator.
6 and 8 both have the common denominator 24. 
6 × 4 = 24
8 × 3 = 24

To change 386 to the common denominator 24, multiply both the numerator and denominator by 4.

38 × 46 × 4 = 15224

To change 558 to the common denominator 24, multiply both the numerator and denominator by 3.

55 × 38 × 3 = 16524

Now compare the numerators:

16524 > 15224 because 165 > 152, so

Pre-requisite Skills

Equivalent Fractions (4.14.5)

Comparing Fractions (4.14.8)

Convert Between Mixed Numbers and Improper Fractions (4.14.11)