Compare 6/7 and 1/3

Comparing fractions like 6/7 and 1/3 (⅓) 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 3. The smallest common multiple of 7 and 3 is 21. Therefore, 21 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 21, multiply both the numerator (top number) and the denominator by 3. This gives:

To convert our second fraction 1/3 to a fraction with a denominator of 21, 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 18 for 18/21 and 7 for 7/21.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 18 (numerator of 3/21) is greater than 7 (numerator of 7/21):

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

1/3 as a decimal = 1/3 = 0.333

Since 0.857 is greater than than 0.333, 6/7 is greater than 1/3.

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