What is 3/29 plus 2/7? (Answer: 79/203)

Exact Answer

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Problem: What is 3/29 plus 2/7?
Formula / Expression: 3/29 + 2/7
Final Answer: 79/203
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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 3/29 by 7, and multiply the numerator and denominator of 2/7 by 29 so both fractions share the common base 203.
Working: 3 × 7/29 × 7 = 21/203 and 2 × 29/7 × 29 = 58/203

Step 3: Add the Numerators
Now add the numerators (21 + 58 = 79) and keep the common denominator 203 unchanged.
Working: 21 + 58/203 = 79/203

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 203 is 1, confirming that 79/203 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/203

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 203 produces a repeating decimal (approximately 0.389163, or 38.9163%).
Working: 79 ÷ 203 = 0.389163 (38.9163%)

Key Values:
- Simplified Fraction: 79/203
- Mixed Number Form: 79/203
- Decimal Value: 0.389163
- Percentage: 38.9163%

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Solved with FractionsCalc:
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3/29 + 2/7 = 79/203

Simplified Fraction

79/203

Mixed Number

Proper (79/203)

Decimal Value

0.389163

Percentage

38.9163%

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Step-by-Step Solution: 3/29 + 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 3/29 by 7, and multiply the numerator and denominator of 2/7 by 29 so both fractions share the common base 203.

3 × 7/29 × 7 = 21/203 and 2 × 29/7 × 29 = 58/203

Step 3

Add the Numerators

Now add the numerators (21 + 58 = 79) and keep the common denominator 203 unchanged.

21 + 58/203 = 79/203

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 203 is 1, confirming that 79/203 cannot be reduced further—it is already in its simplest irreducible form.

79/203

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 203 produces a repeating decimal (approximately 0.389163, or 38.9163%).

79 ÷ 203 = 0.389163 (38.9163%)

Visual Representation

The diagram below illustrates 3/29 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/203`
Mixed Number Form	`79/203`
Decimal Form	`0.389163`
Percentage	`38.9163%`

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Frequently Asked Questions

What is 3/29 plus 2/7 as a fraction?

3/29 + 2/7 in simplest fraction form is 79/203.

What is 3/29 plus 2/7 as a decimal?

3/29 + 2/7 converted to a decimal is 0.389163.

What is 3/29 plus 2/7 as a percentage?

3/29 + 2/7 expressed as a percentage is 38.9163%.

Does 3/29 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.389163...) because the denominator contains prime factors other than 2 and 5.