Is 8/9 Bigger Than 7/12?

Q: Which is bigger: 8/9 or 7/12?

8/9 is bigger. As a decimal, 8/9 = 0.888889 while 7/12 = 0.583333.

Q: What is the difference between 8/9 and 7/12?

The difference is 11/36, which equals 0.305556 in decimal form (30.5556 percentage points).

Yes, 8/9 is bigger than 7/12. Hit Compare below to see the visual breakdown and step-by-step solution — or change the fractions to compare your own.

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How to Compare $\frac{8}{9}$ and $\frac{7}{12}$ Step by Step

Wondering how to figure out which fraction is bigger without a calculator? Comparing $\frac{8}{9}$ and $\frac{7}{12}$ is straightforward once you know the right approach. Below we walk through three proven methods for comparing fractions: finding a common denominator, cross multiplication, and converting to decimals. Each method will give you the same answer, so choose the one that feels easiest.

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 9 and 12, and the least common denominator (LCD) is 36.

Step 1. Convert $\frac{8}{9}$: multiply numerator and denominator by 4. $\frac{8}{9} = \frac{8 \times 4}{9 \times 4} = \frac{32}{36}$
Step 2. Convert $\frac{7}{12}$: multiply numerator and denominator by 3. $\frac{7}{12} = \frac{7 \times 3}{12 \times 3} = \frac{21}{36}$
Step 3. Compare the numerators: 32 vs 21.
Step 4. Since 32 is greater than 21, we know that $\frac{8}{9} > \frac{7}{12}$.

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: $8 \times 12 = 96$.
Step 2. Multiply the numerator of the second fraction by the denominator of the first: $7 \times 9 = 63$.
Step 3. Compare the products: $96 > 63$, so $\frac{8}{9} > \frac{7}{12}$.

Method 3: Decimal Comparison

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

$\frac{8}{9}$ as a decimal 0.888889

$\frac{7}{12}$ as a decimal 0.583333

Difference 0.305556

Since 0.888889 is greater than 0.583333, we confirm that $\frac{8}{9} > \frac{7}{12}$. In percentage terms, $\frac{8}{9}$ is 88.8889% and $\frac{7}{12}$ is 58.3333%, a difference of 30.5556 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 36, we're cutting both quantities into equal-sized pieces. Then 32 pieces vs 21 pieces is a straightforward comparison.

Frequently Asked Questions

Which is bigger: 8/9 or 7/12?

$\frac{8}{9}$ is bigger. As a decimal, $\frac{8}{9}$ = 0.888889 while $\frac{7}{12}$ = 0.583333.

What is the difference between 8/9 and 7/12?

The difference is $\frac{11}{36}$, which equals 0.305556 in decimal form (30.5556 percentage points).

How do you compare 8/9 and 7/12?

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 $\frac{8}{9}$ $>$ $\frac{7}{12}$.

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