Compare 10/13 and 2/6

Comparing fractions like 10/13 and 2/6 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 13 and 6. The smallest common multiple of 13 and 6 is 78. Therefore, 78 will be our common denominator.

Step 2: Convert the Fractions

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

To convert 10/13 to a fraction with a denominator of 78, multiply both the numerator (top number) and the denominator by 6. This gives:

To convert our second fraction 2/6 to a fraction with a denominator of 78, multiply both the numerator and the denominator by 13. This gives:

Step 3: Compare the Numerators

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

The numerators are 60 for 60/78 and 26 for 26/78.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 60 (numerator of 6/78) is greater than 26 (numerator of 13/78):

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).

10/13 as a decimal = 10/13 = 0.769

2/6 as a decimal = 2/6 = 0.333

Since 0.769 is greater than than 0.333, 10/13 is greater than 2/6.