What is 7/29 plus 2/7? (Answer: 107/203)

Exact Answer

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Problem: What is 7/29 plus 2/7?
Formula / Expression: 7/29 + 2/7
Final Answer: 107/203
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 7 = 203.
Working: LCD(29, 7) = 203

Step 2: Convert to Equivalent Fractions with Common Denominator 203
Multiply the numerator and denominator of 7/29 by 7, and multiply the numerator and denominator of 2/7 by 29 so both fractions share the common base 203.
Working: 7 × 7/29 × 7 = 49/203 and 2 × 29/7 × 29 = 58/203

Step 3: Add the Numerators
Now add the numerators (49 + 58 = 107) and keep the common denominator 203 unchanged.
Working: 49 + 58/203 = 107/203

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 203 is 1, confirming that 107/203 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/203

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 203 produces a repeating decimal (approximately 0.527094, or 52.7094%).
Working: 107 ÷ 203 = 0.527094 (52.7094%)

Key Values:
- Simplified Fraction: 107/203
- Mixed Number Form: 107/203
- Decimal Value: 0.527094
- Percentage: 52.7094%

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Solved with FractionsCalc:
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7/29 + 2/7 = 107/203

Simplified Fraction

107/203

Mixed Number

Proper (107/203)

Decimal Value

0.527094

Percentage

52.7094%

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Step-by-Step Solution: 7/29 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 7 = 203.

LCD(29, 7) = 203

Step 2

Convert to Equivalent Fractions with Common Denominator 203

Multiply the numerator and denominator of 7/29 by 7, and multiply the numerator and denominator of 2/7 by 29 so both fractions share the common base 203.

7 × 7/29 × 7 = 49/203 and 2 × 29/7 × 29 = 58/203

Step 3

Add the Numerators

Now add the numerators (49 + 58 = 107) and keep the common denominator 203 unchanged.

49 + 58/203 = 107/203

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 203 is 1, confirming that 107/203 cannot be reduced further—it is already in its simplest irreducible form.

107/203

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 203 produces a repeating decimal (approximately 0.527094, or 52.7094%).

107 ÷ 203 = 0.527094 (52.7094%)

Visual Representation

The diagram below illustrates 7/29 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/203`
Mixed Number Form	`107/203`
Decimal Form	`0.527094`
Percentage	`52.7094%`

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Frequently Asked Questions

What is 7/29 plus 2/7 as a fraction?

7/29 + 2/7 in simplest fraction form is 107/203.

What is 7/29 plus 2/7 as a decimal?

7/29 + 2/7 converted to a decimal is 0.527094.

What is 7/29 plus 2/7 as a percentage?

7/29 + 2/7 expressed as a percentage is 52.7094%.

Does 7/29 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.527094...) because the denominator contains prime factors other than 2 and 5.