Comparing Fractions With Different Denominators
There are two ways to comparing fractions with different denominators.
Method 1: Making the Denominators the Same.
When the denominators are not the same we need to make them the same. For comparing fractions with unlike denominators, we need to convert them to like denominators, for which we should find the Least Common Multiple (LCM) of the denominators. When the denominators are made the same, we can compare the fractions easily.
- Find the least common denominator (LCD).
- Convert the fractions into equivalent fractions with the LCD.
- Since the fractions have similar denominators, compare the numerators.
Example Which is larger: 38 or 712 ?
Answer
Since the fractions have unlike denominators, get the least common denominator (LCD).
8 = 2 × 2 × 2
12 = 2 × 2 × 3
LCD = 2 × 2 × 2 × 3 = 24.
When we multiply 8 × 3 we get 24 and when we multiply 12 × 2 we also get 24. Since the fractions have similar denominators, compare the numerators.
We can now see that 1424 is larger than 924. (Because 14 is larger than 9).
- Convert each fraction to decimals
- Then compare the decimals.
Example Which is smaller: 35 or 410 ?
Answer
35 = 0,6
410 = 0,4
Since 0,4 is smaller than 0,6, therefore 410 is smaller.