What is 3/13 plus 7/29? (Answer: 178/377)

Exact Answer

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Problem: What is 3/13 plus 7/29?
Formula / Expression: 3/13 + 7/29
Final Answer: 178/377
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 29 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 29 = 377.
Working: LCD(13, 29) = 377

Step 2: Convert to Equivalent Fractions with Common Denominator 377
Multiply the numerator and denominator of 3/13 by 29, and multiply the numerator and denominator of 7/29 by 13 so both fractions share the common base 377.
Working: 3 × 29/13 × 29 = 87/377 and 7 × 13/29 × 13 = 91/377

Step 3: Add the Numerators
Now add the numerators (87 + 91 = 178) and keep the common denominator 377 unchanged.
Working: 87 + 91/377 = 178/377

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 178 and 377 is 1, confirming that 178/377 cannot be reduced further—it is already in its simplest irreducible form.
Working: 178/377

Step 5: Decimal & Percentage Representation
Dividing the numerator 178 by denominator 377 produces a repeating decimal (approximately 0.472149, or 47.2149%).
Working: 178 ÷ 377 = 0.472149 (47.2149%)

Key Values:
- Simplified Fraction: 178/377
- Mixed Number Form: 178/377
- Decimal Value: 0.472149
- Percentage: 47.2149%

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Solved with FractionsCalc:
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3/13 + 7/29 = 178/377

Simplified Fraction

178/377

Mixed Number

Proper (178/377)

Decimal Value

0.472149

Percentage

47.2149%

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Step-by-Step Solution: 3/13 + 7/29

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 29 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 29 = 377.

LCD(13, 29) = 377

Step 2

Convert to Equivalent Fractions with Common Denominator 377

Multiply the numerator and denominator of 3/13 by 29, and multiply the numerator and denominator of 7/29 by 13 so both fractions share the common base 377.

3 × 29/13 × 29 = 87/377 and 7 × 13/29 × 13 = 91/377

Step 3

Add the Numerators

Now add the numerators (87 + 91 = 178) and keep the common denominator 377 unchanged.

87 + 91/377 = 178/377

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 178 and 377 is 1, confirming that 178/377 cannot be reduced further—it is already in its simplest irreducible form.

178/377

Step 5

Decimal & Percentage Representation

Dividing the numerator 178 by denominator 377 produces a repeating decimal (approximately 0.472149, or 47.2149%).

178 ÷ 377 = 0.472149 (47.2149%)

Visual Representation

The diagram below illustrates 3/13 plus 7/29 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`178/377`
Mixed Number Form	`178/377`
Decimal Form	`0.472149`
Percentage	`47.2149%`

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Frequently Asked Questions

What is 3/13 plus 7/29 as a fraction?

3/13 + 7/29 in simplest fraction form is 178/377.

What is 3/13 plus 7/29 as a decimal?

3/13 + 7/29 converted to a decimal is 0.472149.

What is 3/13 plus 7/29 as a percentage?

3/13 + 7/29 expressed as a percentage is 47.2149%.

Does 3/13 plus 7/29 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.472149...) because the denominator contains prime factors other than 2 and 5.