What is 2/29 plus 3/7? (Answer: 101/203)

Exact Answer

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Problem: What is 2/29 plus 3/7?
Formula / Expression: 2/29 + 3/7
Final Answer: 101/203
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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 2/29 by 7, and multiply the numerator and denominator of 3/7 by 29 so both fractions share the common base 203.
Working: 2 × 7/29 × 7 = 14/203 and 3 × 29/7 × 29 = 87/203

Step 3: Add the Numerators
Now add the numerators (14 + 87 = 101) and keep the common denominator 203 unchanged.
Working: 14 + 87/203 = 101/203

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 203 is 1, confirming that 101/203 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/203

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 203 produces a repeating decimal (approximately 0.497537, or 49.7537%).
Working: 101 ÷ 203 = 0.497537 (49.7537%)

Key Values:
- Simplified Fraction: 101/203
- Mixed Number Form: 101/203
- Decimal Value: 0.497537
- Percentage: 49.7537%

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2/29 + 3/7 = 101/203

Simplified Fraction

101/203

Mixed Number

Proper (101/203)

Decimal Value

0.497537

Percentage

49.7537%

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Step-by-Step Solution: 2/29 + 3/7

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

2 × 7/29 × 7 = 14/203 and 3 × 29/7 × 29 = 87/203

Step 3

Add the Numerators

Now add the numerators (14 + 87 = 101) and keep the common denominator 203 unchanged.

14 + 87/203 = 101/203

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 203 is 1, confirming that 101/203 cannot be reduced further—it is already in its simplest irreducible form.

101/203

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 203 produces a repeating decimal (approximately 0.497537, or 49.7537%).

101 ÷ 203 = 0.497537 (49.7537%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/203`
Mixed Number Form	`101/203`
Decimal Form	`0.497537`
Percentage	`49.7537%`

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Frequently Asked Questions

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

2/29 + 3/7 in simplest fraction form is 101/203.

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

2/29 + 3/7 converted to a decimal is 0.497537.

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

2/29 + 3/7 expressed as a percentage is 49.7537%.

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

It results in a repeating decimal (approximately 0.497537...) because the denominator contains prime factors other than 2 and 5.