What is 2/7 plus 8/25? (Answer: 106/175)

Exact Answer

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Problem: What is 2/7 plus 8/25?
Formula / Expression: 2/7 + 8/25
Final Answer: 106/175
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 175
Multiply the numerator and denominator of 2/7 by 25, and multiply the numerator and denominator of 8/25 by 7 so both fractions share the common base 175.
Working: 2 × 25/7 × 25 = 50/175 and 8 × 7/25 × 7 = 56/175

Step 3: Add the Numerators
Now add the numerators (50 + 56 = 106) and keep the common denominator 175 unchanged.
Working: 50 + 56/175 = 106/175

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 106 and 175 is 1, confirming that 106/175 cannot be reduced further—it is already in its simplest irreducible form.
Working: 106/175

Step 5: Decimal & Percentage Representation
Dividing the numerator 106 by denominator 175 produces a repeating decimal (approximately 0.605714, or 60.5714%).
Working: 106 ÷ 175 = 0.605714 (60.5714%)

Key Values:
- Simplified Fraction: 106/175
- Mixed Number Form: 106/175
- Decimal Value: 0.605714
- Percentage: 60.5714%

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Solved with FractionsCalc:
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2/7 + 8/25 = 106/175

Simplified Fraction

106/175

Mixed Number

Proper (106/175)

Decimal Value

0.605714

Percentage

60.5714%

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Step-by-Step Solution: 2/7 + 8/25

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 25) = 175

Step 2

Convert to Equivalent Fractions with Common Denominator 175

Multiply the numerator and denominator of 2/7 by 25, and multiply the numerator and denominator of 8/25 by 7 so both fractions share the common base 175.

2 × 25/7 × 25 = 50/175 and 8 × 7/25 × 7 = 56/175

Step 3

Add the Numerators

Now add the numerators (50 + 56 = 106) and keep the common denominator 175 unchanged.

50 + 56/175 = 106/175

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 106 and 175 is 1, confirming that 106/175 cannot be reduced further—it is already in its simplest irreducible form.

106/175

Step 5

Decimal & Percentage Representation

Dividing the numerator 106 by denominator 175 produces a repeating decimal (approximately 0.605714, or 60.5714%).

106 ÷ 175 = 0.605714 (60.5714%)

Visual Representation

The diagram below illustrates 2/7 plus 8/25 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`106/175`
Mixed Number Form	`106/175`
Decimal Form	`0.605714`
Percentage	`60.5714%`

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Frequently Asked Questions

What is 2/7 plus 8/25 as a fraction?

2/7 + 8/25 in simplest fraction form is 106/175.

What is 2/7 plus 8/25 as a decimal?

2/7 + 8/25 converted to a decimal is 0.605714.

What is 2/7 plus 8/25 as a percentage?

2/7 + 8/25 expressed as a percentage is 60.5714%.

Does 2/7 plus 8/25 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.605714...) because the denominator contains prime factors other than 2 and 5.