What is 2/25 plus 4/7? (Answer: 114/175)

Exact Answer

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Problem: What is 2/25 plus 4/7?
Formula / Expression: 2/25 + 4/7
Final Answer: 114/175
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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 4/7 by 25 so both fractions share the common base 175.
Working: 2 × 7/25 × 7 = 14/175 and 4 × 25/7 × 25 = 100/175

Step 3: Add the Numerators
Now add the numerators (14 + 100 = 114) and keep the common denominator 175 unchanged.
Working: 14 + 100/175 = 114/175

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 114 and 175 is 1, confirming that 114/175 cannot be reduced further—it is already in its simplest irreducible form.
Working: 114/175

Step 5: Decimal & Percentage Representation
Dividing the numerator 114 by denominator 175 produces a repeating decimal (approximately 0.651429, or 65.1429%).
Working: 114 ÷ 175 = 0.651429 (65.1429%)

Key Values:
- Simplified Fraction: 114/175
- Mixed Number Form: 114/175
- Decimal Value: 0.651429
- Percentage: 65.1429%

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Solved with FractionsCalc:
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2/25 + 4/7 = 114/175

Simplified Fraction

114/175

Mixed Number

Proper (114/175)

Decimal Value

0.651429

Percentage

65.1429%

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Step-by-Step Solution: 2/25 + 4/7

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 4/7 by 25 so both fractions share the common base 175.

2 × 7/25 × 7 = 14/175 and 4 × 25/7 × 25 = 100/175

Step 3

Add the Numerators

Now add the numerators (14 + 100 = 114) and keep the common denominator 175 unchanged.

14 + 100/175 = 114/175

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 114 and 175 is 1, confirming that 114/175 cannot be reduced further—it is already in its simplest irreducible form.

114/175

Step 5

Decimal & Percentage Representation

Dividing the numerator 114 by denominator 175 produces a repeating decimal (approximately 0.651429, or 65.1429%).

114 ÷ 175 = 0.651429 (65.1429%)

Visual Representation

The diagram below illustrates 2/25 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`114/175`
Mixed Number Form	`114/175`
Decimal Form	`0.651429`
Percentage	`65.1429%`

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Frequently Asked Questions

What is 2/25 plus 4/7 as a fraction?

2/25 + 4/7 in simplest fraction form is 114/175.

What is 2/25 plus 4/7 as a decimal?

2/25 + 4/7 converted to a decimal is 0.651429.

What is 2/25 plus 4/7 as a percentage?

2/25 + 4/7 expressed as a percentage is 65.1429%.

Does 2/25 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.651429...) because the denominator contains prime factors other than 2 and 5.