Compare 5/7 and 6/15

Comparing fractions like 5/7 and 6/15 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 15. The smallest common multiple of 7 and 15 is 105. Therefore, 105 will be our common denominator.

Step 2: Convert the Fractions

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

To convert 5/7 to a fraction with a denominator of 105, multiply both the numerator (top number) and the denominator by 15. This gives:

To convert our second fraction 6/15 to a fraction with a denominator of 105, multiply both the numerator and the denominator by 7. This gives:

Step 3: Compare the Numerators

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

The numerators are 75 for 75/105 and 42 for 42/105.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 75 (numerator of 15/105) is greater than 42 (numerator of 7/105):

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).

5/7 as a decimal = 5/7 = 0.714

6/15 as a decimal = 6/15 = 0.4

Since 0.714 is greater than than 0.4, 5/7 is greater than 6/15.