Explain Comparing Fractions with example?

If fractions are not equivalent, how do you figure out which one is larger?

Comparing fractions involves finding the least common multiple of the denominators, called LCD (Least Common Denominator).
To compare fractions:

First, convert the fractions to equivalent fractions having the LCD.

Second, compare the numerators of the fractions.

The fraction with the larger numerator is larger.

Example: Compare 7/15 and 4/10.

Step 1: Find the LCM of 15 and 10.
Multiples of 15: 15, 30, 45, 60, ...
Multiples of 10: 10, 20, 30, 40, 50 , 60,...
The smallest multiple they have in common is 30.
Therefore, the LCD of the fractions is 30.

Step 2: Write the equivalent fractions of 7/15 and 4/10 having denominator 30.
7/15 = 7x2/15x2 = 14/30
To change 15 to 30, 15 must be multiplied by 2. If the denominator is multiplied by 2, then the numerator must be multiplied by 2.

Remember: Multiplying or dividing the numerator and denominator by the same number makes equivalent fractions.
4/10 = 4x3/10x3 =12/30

To change 10 to 30, 10 must be multiplied 3. So, the numerator, 4 must be multiplied by 3.

Step 3: Compare the numerators of the equivalent fractions.
7/15?4/10
14/30?12/30
14/30>12/30
7/15>4/10

Since 14/30 and 12/30 have the same denominators, the larger fraction has the larger numerator.

14/30 is larger. 14/30 is the same as 7/15.

Therefore, 7/15 is the larger fraction.