Compare 7/8 and 11/13

Comparing fractions like 7/8 (⅞) and 11/13 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 8 and 13. The smallest common multiple of 8 and 13 is 104. Therefore, 104 will be our common denominator.

Step 2: Convert the Fractions

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

To convert 7/8 to a fraction with a denominator of 104, multiply both the numerator (top number) and the denominator by 13. This gives:

To convert our second fraction 11/13 to a fraction with a denominator of 104, multiply both the numerator and the denominator by 8. This gives:

Step 3: Compare the Numerators

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

The numerators are 91 for 91/104 and 88 for 88/104.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 91 (numerator of 13/104) is greater than 88 (numerator of 8/104):

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).

7/8 as a decimal = 7/8 = 0.875

11/13 as a decimal = 11/13 = 0.846

Since 0.875 is greater than than 0.846, 7/8 is greater than 11/13.