Compare 10/11 and 10/13

Comparing fractions like 10/11 and 10/13 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 11 and 13. The smallest common multiple of 11 and 13 is 143. Therefore, 143 will be our common denominator.

Step 2: Convert the Fractions

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

To convert 10/11 to a fraction with a denominator of 143, multiply both the numerator (top number) and the denominator by 13. This gives:

To convert our second fraction 10/13 to a fraction with a denominator of 143, multiply both the numerator and the denominator by 11. This gives:

Step 3: Compare the Numerators

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

The numerators are 130 for 130/143 and 110 for 110/143.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 130 (numerator of 13/143) is greater than 110 (numerator of 11/143):

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).

10/11 as a decimal = 10/11 = 0.909

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

Since 0.909 is greater than than 0.769, 10/11 is greater than 10/13.

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