What is 2/25 plus 3/7? (Answer: 89/175)

Exact Answer

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Problem: What is 2/25 plus 3/7?
Formula / Expression: 2/25 + 3/7
Final Answer: 89/175
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 7 = 175.
Working: LCD(25, 7) = 175

Step 2: Convert to Equivalent Fractions with Common Denominator 175
Multiply the numerator and denominator of 2/25 by 7, and multiply the numerator and denominator of 3/7 by 25 so both fractions share the common base 175.
Working: 2 × 7/25 × 7 = 14/175 and 3 × 25/7 × 25 = 75/175

Step 3: Add the Numerators
Now add the numerators (14 + 75 = 89) and keep the common denominator 175 unchanged.
Working: 14 + 75/175 = 89/175

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 175 is 1, confirming that 89/175 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/175

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 175 produces a repeating decimal (approximately 0.508571, or 50.8571%).
Working: 89 ÷ 175 = 0.508571 (50.8571%)

Key Values:
- Simplified Fraction: 89/175
- Mixed Number Form: 89/175
- Decimal Value: 0.508571
- Percentage: 50.8571%

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Solved with FractionsCalc:
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2/25 + 3/7 = 89/175

Simplified Fraction

89/175

Mixed Number

Proper (89/175)

Decimal Value

0.508571

Percentage

50.8571%

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Step-by-Step Solution: 2/25 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 7 = 175.

LCD(25, 7) = 175

Step 2

Convert to Equivalent Fractions with Common Denominator 175

Multiply the numerator and denominator of 2/25 by 7, and multiply the numerator and denominator of 3/7 by 25 so both fractions share the common base 175.

2 × 7/25 × 7 = 14/175 and 3 × 25/7 × 25 = 75/175

Step 3

Add the Numerators

Now add the numerators (14 + 75 = 89) and keep the common denominator 175 unchanged.

14 + 75/175 = 89/175

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 175 is 1, confirming that 89/175 cannot be reduced further—it is already in its simplest irreducible form.

89/175

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 175 produces a repeating decimal (approximately 0.508571, or 50.8571%).

89 ÷ 175 = 0.508571 (50.8571%)

Visual Representation

The diagram below illustrates 2/25 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/175`
Mixed Number Form	`89/175`
Decimal Form	`0.508571`
Percentage	`50.8571%`

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Frequently Asked Questions

What is 2/25 plus 3/7 as a fraction?

2/25 + 3/7 in simplest fraction form is 89/175.

What is 2/25 plus 3/7 as a decimal?

2/25 + 3/7 converted to a decimal is 0.508571.

What is 2/25 plus 3/7 as a percentage?

2/25 + 3/7 expressed as a percentage is 50.8571%.

Does 2/25 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.508571...) because the denominator contains prime factors other than 2 and 5.