Compare 6/7 and 6/10

Comparing fractions like 6/7 and 6/10 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 10. The smallest common multiple of 7 and 10 is 70. Therefore, 70 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 70, multiply both the numerator (top number) and the denominator by 10. This gives:

To convert our second fraction 6/10 to a fraction with a denominator of 70, 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 60 for 60/70 and 42 for 42/70.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 60 (numerator of 10/70) is greater than 42 (numerator of 7/70):

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

6/10 as a decimal = 6/10 = 0.6

Since 0.857 is greater than than 0.6, 6/7 is greater than 6/10.

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