Compare 1/6 and 5/7

Comparing fractions like 1/6 (⅙) and 5/7 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 6 and 7. The smallest common multiple of 6 and 7 is 42. Therefore, 42 will be our common denominator.

Step 2: Convert the Fractions

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

To convert 1/6 to a fraction with a denominator of 42, multiply both the numerator (top number) and the denominator by 7. This gives:

To convert our second fraction 5/7 to a fraction with a denominator of 42, multiply both the numerator and the denominator by 6. This gives:

Step 3: Compare the Numerators

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

The numerators are 7 for 7/42 and 30 for 30/42.

Step 4: Determine the Larger Fraction

The fraction with the larger numerator is the greater fraction.

Since 7 (numerator of 7/42) is not greater than 30 (numerator of 6/42):

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).

1/6 as a decimal = 1/6 = 0.167

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

Since 0.167 is not greater than than 0.714, 1/6 is not greater than 5/7.

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