What is 2/25 plus 7/9? (Answer: 193/225)

Exact Answer

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Problem: What is 2/25 plus 7/9?
Formula / Expression: 2/25 + 7/9
Final Answer: 193/225
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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 2/25 by 9, and multiply the numerator and denominator of 7/9 by 25 so both fractions share the common base 225.
Working: 2 × 9/25 × 9 = 18/225 and 7 × 25/9 × 25 = 175/225

Step 3: Add the Numerators
Now add the numerators (18 + 175 = 193) and keep the common denominator 225 unchanged.
Working: 18 + 175/225 = 193/225

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 193 and 225 is 1, confirming that 193/225 cannot be reduced further—it is already in its simplest irreducible form.
Working: 193/225

Step 5: Decimal & Percentage Representation
Dividing the numerator 193 by denominator 225 produces a repeating decimal (approximately 0.857778, or 85.7778%).
Working: 193 ÷ 225 = 0.857778 (85.7778%)

Key Values:
- Simplified Fraction: 193/225
- Mixed Number Form: 193/225
- Decimal Value: 0.857778
- Percentage: 85.7778%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-25-plus-7-9/
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2/25 + 7/9 = 193/225

Simplified Fraction

193/225

Mixed Number

Proper (193/225)

Decimal Value

0.857778

Percentage

85.7778%

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Step-by-Step Solution: 2/25 + 7/9

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 2/25 by 9, and multiply the numerator and denominator of 7/9 by 25 so both fractions share the common base 225.

2 × 9/25 × 9 = 18/225 and 7 × 25/9 × 25 = 175/225

Step 3

Add the Numerators

Now add the numerators (18 + 175 = 193) and keep the common denominator 225 unchanged.

18 + 175/225 = 193/225

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 193 and 225 is 1, confirming that 193/225 cannot be reduced further—it is already in its simplest irreducible form.

193/225

Step 5

Decimal & Percentage Representation

Dividing the numerator 193 by denominator 225 produces a repeating decimal (approximately 0.857778, or 85.7778%).

193 ÷ 225 = 0.857778 (85.7778%)

Visual Representation

The diagram below illustrates 2/25 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`193/225`
Mixed Number Form	`193/225`
Decimal Form	`0.857778`
Percentage	`85.7778%`

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Frequently Asked Questions

What is 2/25 plus 7/9 as a fraction?

2/25 + 7/9 in simplest fraction form is 193/225.

What is 2/25 plus 7/9 as a decimal?

2/25 + 7/9 converted to a decimal is 0.857778.

What is 2/25 plus 7/9 as a percentage?

2/25 + 7/9 expressed as a percentage is 85.7778%.

Does 2/25 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.857778...) because the denominator contains prime factors other than 2 and 5.