A fraction consists of two numbers separated by a line represented as a/b. It represents the parts of a whole. The top number, called numerator, tells how many parts there are and the bottom number, called denominator, tells the total number of parts the object is divided into.
Fractions with different (unlike) denominators are also called unlike fractions. There are various methods to compare fractions with unlike denominators.
1. Decimal method: In this method each fraction is converted to equivalent decimal and then compared.
Example:
Compare 3/5 and 4/9
3/5 = 0.6 and 4/9 = 0.44
So, 3/5 > 4/9
2. Common denominator method: We can make the denominators same by finding the common multiple of the two denominators. Then make the denominators of both the fractions equal to the common multiple. Make sure to multiply the numerator with the same factor with which denominator is multiplied. Let us take the above example once again.
3/5 and 4/9
Common multiple of 5 and 9 is 45.
Multiply both numerator and denominator of 3/5 by 9 so that denominator is 45. Also, multiply both numerator and denominator of 4/9 by 5 so that denominator is 45.
(3 × 9)/(5 × 9) and (4 × 5)/(9 × 5)
27/45 and 20/45
Now, both the fractions have same denominators. As we know the fraction with greater numerator is the greater fraction.
So, 27/45 > 20/45
i.e. 3/5 > 4/9
Another way of making denominators same is by multiplying first fraction (both numerator and denominator) by the denominator of second fraction and multiplying second fraction (both numerator and denominator) by denominator of first fraction like demonstrated in the above example.
3. Cross multiplication: Find the first cross-product by multiplying first numerator by second denominator. Then, find the second cross-product by multiplying second numerator by first denominator. If the cross products are equal, the fractions are equal. If the first cross-product is greater, the first fraction is greater and if the second cross-product is greater the second fraction is greater.
Example:
3/7 and 4/5
First cross-product: 3 × 5 = 15
Second cross-product: 4 × 7 = 28
Since the second cross-product is greater, the second fraction 4/5 is greater than 3/7.
Let’s compare the fractions compared in the other two methods now using the cross multiplication method.
3/5 and 4/9
First cross-product: 3 × 9 = 27
Second cross-product: 4 × 5 = 20
Since first cross product is greater, the first fraction 3/5 is greater than 4/9