Compare 2/9 and 2/13

Comparing fractions like 2/9 and 2/13 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 13. The smallest common multiple of 9 and 13 is 117. Therefore, 117 will be our common denominator.

Step 2: Convert the Fractions

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

To convert 2/9 to a fraction with a denominator of 117, multiply both the numerator (top number) and the denominator by 13. This gives:

To convert our second fraction 2/13 to a fraction with a denominator of 117, 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 26 for 26/117 and 18 for 18/117.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 26 (numerator of 13/117) is greater than 18 (numerator of 9/117):

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).

2/9 as a decimal = 2/9 = 0.222

2/13 as a decimal = 2/13 = 0.154

Since 0.222 is greater than than 0.154, 2/9 is greater than 2/13.

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