Compare 10/13 and 3/7

Comparing fractions like 10/13 and 3/7 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 7. The smallest common multiple of 13 and 7 is 91. Therefore, 91 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 91, multiply both the numerator (top number) and the denominator by 7. This gives:

To convert our second fraction 3/7 to a fraction with a denominator of 91, 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 70 for 70/91 and 39 for 39/91.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 70 (numerator of 7/91) is greater than 39 (numerator of 13/91):

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

3/7 as a decimal = 3/7 = 0.429

Since 0.769 is greater than than 0.429, 10/13 is greater than 3/7.