What is 7/25 plus 2/7? (Answer: 99/175)

Exact Answer

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Problem: What is 7/25 plus 2/7?
Formula / Expression: 7/25 + 2/7
Final Answer: 99/175
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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 7/25 by 7, and multiply the numerator and denominator of 2/7 by 25 so both fractions share the common base 175.
Working: 7 × 7/25 × 7 = 49/175 and 2 × 25/7 × 25 = 50/175

Step 3: Add the Numerators
Now add the numerators (49 + 50 = 99) and keep the common denominator 175 unchanged.
Working: 49 + 50/175 = 99/175

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 99 and 175 is 1, confirming that 99/175 cannot be reduced further—it is already in its simplest irreducible form.
Working: 99/175

Step 5: Decimal & Percentage Representation
Dividing the numerator 99 by denominator 175 produces a repeating decimal (approximately 0.565714, or 56.5714%).
Working: 99 ÷ 175 = 0.565714 (56.5714%)

Key Values:
- Simplified Fraction: 99/175
- Mixed Number Form: 99/175
- Decimal Value: 0.565714
- Percentage: 56.5714%

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Solved with FractionsCalc:
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7/25 + 2/7 = 99/175

Simplified Fraction

99/175

Mixed Number

Proper (99/175)

Decimal Value

0.565714

Percentage

56.5714%

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

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

7 × 7/25 × 7 = 49/175 and 2 × 25/7 × 25 = 50/175

Step 3

Add the Numerators

Now add the numerators (49 + 50 = 99) and keep the common denominator 175 unchanged.

49 + 50/175 = 99/175

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 99 and 175 is 1, confirming that 99/175 cannot be reduced further—it is already in its simplest irreducible form.

99/175

Step 5

Decimal & Percentage Representation

Dividing the numerator 99 by denominator 175 produces a repeating decimal (approximately 0.565714, or 56.5714%).

99 ÷ 175 = 0.565714 (56.5714%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`99/175`
Mixed Number Form	`99/175`
Decimal Form	`0.565714`
Percentage	`56.5714%`

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Frequently Asked Questions

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

7/25 + 2/7 in simplest fraction form is 99/175.

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

7/25 + 2/7 converted to a decimal is 0.565714.

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

7/25 + 2/7 expressed as a percentage is 56.5714%.

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

It results in a repeating decimal (approximately 0.565714...) because the denominator contains prime factors other than 2 and 5.