Is 5/9 Bigger Than 7/9?

Q: Which is bigger: 5/9 or 7/9?

7/9 is bigger. As a decimal, 7/9 = 0.777778 while 5/9 = 0.555556.

Q: What is the difference between 5/9 and 7/9?

The difference is 2/9, which equals 0.222222 in decimal form (22.2222 percentage points).

Q: How do you compare 5/9 and 7/9?

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 7/9 is greater than 5/9.

No, \(\frac{5}{9}\) < \(\frac{7}{9}\)

\(\frac{5}{9}\)

55.5556%

\(\frac{7}{9}\)

77.7778%

Method 1: Common Denominators

These fractions already share the same denominator: 9. We just need to compare the numerators.

Step 1. Both fractions already have the same denominator: 9.
Step 2. Compare the numerators: 5 vs 7.
Step 3. Since 5 is less than 7, we know that \(\frac{5}{9} < \frac{7}{9}\).

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: \(5 \times 9 = 45\).
Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(7 \times 9 = 63\).
Step 3. Compare the products: \(45 < 63\), so \(\frac{5}{9} < \frac{7}{9}\).

Method 3: Decimal Comparison

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

\(\frac{5}{9}\) as a decimal 0.555556

\(\frac{7}{9}\) as a decimal 0.777778

Difference 0.222222

Since 0.555556 is less than 0.777778, we confirm that \(\frac{5}{9} < \frac{7}{9}\). In percentage terms, \(\frac{5}{9}\) is 55.5556% and \(\frac{7}{9}\) is 77.7778%, a difference of 22.2222 percentage points.

Why Does This Work?

When two fractions share the same denominator, the pieces are the same size. A fraction with more pieces (a larger numerator) is simply a larger amount. Since 7 pieces is more than 5 pieces of the same size, \(\frac{7}{9}\) is the larger fraction.

Frequently Asked Questions

Which is bigger: 5/9 or 7/9?

\(\frac{7}{9}\) is bigger. As a decimal, \(\frac{7}{9}\) = 0.777778 while \(\frac{5}{9}\) = 0.555556.

What is the difference between 5/9 and 7/9?

The difference is \(\frac{2}{9}\), which equals 0.222222 in decimal form (22.2222 percentage points).

How do you compare 5/9 and 7/9?

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 \(\frac{7}{9}\) \(>\) \(\frac{5}{9}\).

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