Compare 6/9 and 2/5

Comparing fractions like 6/9 and 2/5 (⅖) involves determining which fraction is greater or if they are equal. Here are the steps to compare these fractions:

Step 1: Find a Common Denominator

The first step is to find a common denominator for the fractions. The denominator is the bottom number in a fraction. A common denominator is a number that both denominators can divide into without a remainder. In this case, the denominators are 9 and 5. The smallest common multiple of 9 and 5 is 45. Therefore, 45 will be our common denominator.

Step 2: Convert the Fractions

Next, convert each fraction to an equivalent fraction with the common denominator.

To convert 6/9 to a fraction with a denominator of 45, multiply both the numerator (top number) and the denominator by 5. This gives:

To convert our second fraction 2/5 to a fraction with a denominator of 45, multiply both the numerator and the denominator by 9. This gives:

Step 3: Compare the Numerators

Now that the fractions have the same denominator, you can directly compare their numerators.

The numerators are 30 for 30/45 and 18 for 18/45.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 30 (numerator of 5/45) is greater than 18 (numerator of 9/45):

Conclusion

Therefore,

Another way to figure out which fraction is larger is to convert them into decimal numbers.

To convert a fraction to a decimal, you divide the numerator (top number) by the denominator (bottom number).

6/9 as a decimal = 6/9 = 0.667

2/5 as a decimal = 2/5 = 0.4

Since 0.667 is greater than than 0.4, 6/9 is greater than 2/5.