Compare 6/7 and 11/14

Comparing fractions like 6/7 and 11/14 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 7 and 14. The smallest common multiple of 7 and 14 is 14. Therefore, 14 will be our common denominator.

Step 2: Convert the Fractions

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

To convert 6/7 to a fraction with a denominator of 14, multiply both the numerator (top number) and the denominator by 2. This gives:

To convert our second fraction 11/14 to a fraction with a denominator of 14, multiply both the numerator and the denominator by 1. This gives:

Step 3: Compare the Numerators

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

The numerators are 12 for 12/14 and 11 for 11/14.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 12 (numerator of 2/14) is greater than 11 (numerator of 1/14):

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).

6/7 as a decimal = 6/7 = 0.857

11/14 as a decimal = 11/14 = 0.786

Since 0.857 is greater than than 0.786, 6/7 is greater than 11/14.