What is 8/25 plus 4/9? (Answer: 172/225)

Exact Answer

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Problem: What is 8/25 plus 4/9?
Formula / Expression: 8/25 + 4/9
Final Answer: 172/225
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 9 = 225.
Working: LCD(25, 9) = 225

Step 2: Convert to Equivalent Fractions with Common Denominator 225
Multiply the numerator and denominator of 8/25 by 9, and multiply the numerator and denominator of 4/9 by 25 so both fractions share the common base 225.
Working: 8 × 9/25 × 9 = 72/225 and 4 × 25/9 × 25 = 100/225

Step 3: Add the Numerators
Now add the numerators (72 + 100 = 172) and keep the common denominator 225 unchanged.
Working: 72 + 100/225 = 172/225

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 172 and 225 is 1, confirming that 172/225 cannot be reduced further—it is already in its simplest irreducible form.
Working: 172/225

Step 5: Decimal & Percentage Representation
Dividing the numerator 172 by denominator 225 produces a repeating decimal (approximately 0.764444, or 76.4444%).
Working: 172 ÷ 225 = 0.764444 (76.4444%)

Key Values:
- Simplified Fraction: 172/225
- Mixed Number Form: 172/225
- Decimal Value: 0.764444
- Percentage: 76.4444%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-25-plus-4-9/
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8/25 + 4/9 = 172/225

Simplified Fraction

172/225

Mixed Number

Proper (172/225)

Decimal Value

0.764444

Percentage

76.4444%

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Step-by-Step Solution: 8/25 + 4/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 9 = 225.

LCD(25, 9) = 225

Step 2

Convert to Equivalent Fractions with Common Denominator 225

Multiply the numerator and denominator of 8/25 by 9, and multiply the numerator and denominator of 4/9 by 25 so both fractions share the common base 225.

8 × 9/25 × 9 = 72/225 and 4 × 25/9 × 25 = 100/225

Step 3

Add the Numerators

Now add the numerators (72 + 100 = 172) and keep the common denominator 225 unchanged.

72 + 100/225 = 172/225

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 172 and 225 is 1, confirming that 172/225 cannot be reduced further—it is already in its simplest irreducible form.

172/225

Step 5

Decimal & Percentage Representation

Dividing the numerator 172 by denominator 225 produces a repeating decimal (approximately 0.764444, or 76.4444%).

172 ÷ 225 = 0.764444 (76.4444%)

Visual Representation

The diagram below illustrates 8/25 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`172/225`
Mixed Number Form	`172/225`
Decimal Form	`0.764444`
Percentage	`76.4444%`

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Frequently Asked Questions

What is 8/25 plus 4/9 as a fraction?

8/25 + 4/9 in simplest fraction form is 172/225.

What is 8/25 plus 4/9 as a decimal?

8/25 + 4/9 converted to a decimal is 0.764444.

What is 8/25 plus 4/9 as a percentage?

8/25 + 4/9 expressed as a percentage is 76.4444%.

Does 8/25 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.764444...) because the denominator contains prime factors other than 2 and 5.