Is 6/7 Bigger Than 10/11?

Q: Which is bigger: 6/7 or 10/11?

10/11 is bigger. As a decimal, 10/11 = 0.909091 while 6/7 = 0.857143.

Q: What is the difference between 6/7 and 10/11?

The difference is 4/77, which equals 0.051948 in decimal form (5.1948 percentage points).

Q: How do you compare 6/7 and 10/11?

You can use three methods: find a common denominator and compare numerators, cross-multiply and compare the products, or convert both fractions to decimals. All three methods confirm that 10/11 is greater than 6/7.

No, $\frac{6}{7}$ < $\frac{10}{11}$

$\frac{6}{7}$

85.7143%

$\frac{10}{11}$

90.9091%

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 7 and 11, and the least common denominator (LCD) is 77.

Step 1. Convert $\frac{6}{7}$: multiply numerator and denominator by 11. $\frac{6}{7} = \frac{6 \times 11}{7 \times 11} = \frac{66}{77}$
Step 2. Convert $\frac{10}{11}$: multiply numerator and denominator by 7. $\frac{10}{11} = \frac{10 \times 7}{11 \times 7} = \frac{70}{77}$
Step 3. Compare the numerators: 66 vs 70.
Step 4. Since 66 is less than 70, we know that $\frac{6}{7} < \frac{10}{11}$.

Method 2: Cross Multiplication

A quicker way to compare fractions is to cross-multiply. Multiply each numerator by the other fraction's denominator:

Step 1. Multiply the numerator of the first fraction by the denominator of the second: $6 \times 11 = 66$.
Step 2. Multiply the numerator of the second fraction by the denominator of the first: $10 \times 7 = 70$.
Step 3. Compare the products: $66 < 70$, so $\frac{6}{7} < \frac{10}{11}$.

Method 3: Decimal Comparison

Convert each fraction to a decimal by dividing the numerator by the denominator:

$\frac{6}{7}$ as a decimal 0.857143

$\frac{10}{11}$ as a decimal 0.909091

Difference 0.051948

Since 0.857143 is less than 0.909091, we confirm that $\frac{6}{7} < \frac{10}{11}$. In percentage terms, $\frac{6}{7}$ is 85.7143% and $\frac{10}{11}$ is 90.9091%, a difference of 5.1948 percentage points.

Why Does This Work?

These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 77, we're cutting both quantities into equal-sized pieces. Then 66 pieces vs 70 pieces is a straightforward comparison.

Frequently Asked Questions

Which is bigger: 6/7 or 10/11?

$\frac{10}{11}$ is bigger. As a decimal, $\frac{10}{11}$ = 0.909091 while $\frac{6}{7}$ = 0.857143.

What is the difference between 6/7 and 10/11?

The difference is $\frac{4}{77}$, which equals 0.051948 in decimal form (5.1948 percentage points).

How do you compare 6/7 and 10/11?

You can use three methods: find a common denominator and compare numerators, cross-multiply and compare the products, or convert both fractions to decimals. All three methods confirm that $\frac{10}{11}$ $>$ $\frac{6}{7}$.

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