Is 6/7 Bigger Than 7/8?

Q: Which is bigger: 6/7 or 7/8?

7/8 is bigger. As a decimal, 7/8 = 0.875 while 6/7 = 0.857143.

Q: What is the difference between 6/7 and 7/8?

The difference is 1/56, which equals 0.017857 in decimal form (1.7857 percentage points).

Q: How do you compare 6/7 and 7/8?

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 7/8 is greater than 6/7.

No, $\frac{6}{7}$ < $\frac{7}{8}$

$\frac{6}{7}$

85.7143%

$\frac{7}{8}$

87.5%

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 7 and 8, and the least common denominator (LCD) is 56.

Step 1. Convert $\frac{6}{7}$: multiply numerator and denominator by 8. $\frac{6}{7} = \frac{6 \times 8}{7 \times 8} = \frac{48}{56}$
Step 2. Convert $\frac{7}{8}$: multiply numerator and denominator by 7. $\frac{7}{8} = \frac{7 \times 7}{8 \times 7} = \frac{49}{56}$
Step 3. Compare the numerators: 48 vs 49.
Step 4. Since 48 is less than 49, we know that $\frac{6}{7} < \frac{7}{8}$.

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: $6 \times 8 = 48$.
Step 2. Multiply the numerator of the second fraction by the denominator of the first: $7 \times 7 = 49$.
Step 3. Compare the products: $48 < 49$, so $\frac{6}{7} < \frac{7}{8}$.

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

$\frac{7}{8}$ as a decimal 0.875

Difference 0.017857

Since 0.857143 is less than 0.875, we confirm that $\frac{6}{7} < \frac{7}{8}$. In percentage terms, $\frac{6}{7}$ is 85.7143% and $\frac{7}{8}$ is 87.5%, a difference of 1.7857 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 56, we're cutting both quantities into equal-sized pieces. Then 48 pieces vs 49 pieces is a straightforward comparison.

Frequently Asked Questions

Which is bigger: 6/7 or 7/8?

$\frac{7}{8}$ is bigger. As a decimal, $\frac{7}{8}$ = 0.875 while $\frac{6}{7}$ = 0.857143.

What is the difference between 6/7 and 7/8?

The difference is $\frac{1}{56}$, which equals 0.017857 in decimal form (1.7857 percentage points).

How do you compare 6/7 and 7/8?

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 $\frac{7}{8}$ $>$ $\frac{6}{7}$.

Keep Learning

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