What is 9/29 plus 3/8? (Answer: 159/232)

Exact Answer

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Problem: What is 9/29 plus 3/8?
Formula / Expression: 9/29 + 3/8
Final Answer: 159/232
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 8 = 232.
Working: LCD(29, 8) = 232

Step 2: Convert to Equivalent Fractions with Common Denominator 232
Multiply the numerator and denominator of 9/29 by 8, and multiply the numerator and denominator of 3/8 by 29 so both fractions share the common base 232.
Working: 9 × 8/29 × 8 = 72/232 and 3 × 29/8 × 29 = 87/232

Step 3: Add the Numerators
Now add the numerators (72 + 87 = 159) and keep the common denominator 232 unchanged.
Working: 72 + 87/232 = 159/232

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 159 and 232 is 1, confirming that 159/232 cannot be reduced further—it is already in its simplest irreducible form.
Working: 159/232

Step 5: Decimal & Percentage Representation
Dividing the numerator 159 by denominator 232 produces a repeating decimal (approximately 0.685345, or 68.5345%).
Working: 159 ÷ 232 = 0.685345 (68.5345%)

Key Values:
- Simplified Fraction: 159/232
- Mixed Number Form: 159/232
- Decimal Value: 0.685345
- Percentage: 68.5345%

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Solved with FractionsCalc:
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9/29 + 3/8 = 159/232

Simplified Fraction

159/232

Mixed Number

Proper (159/232)

Decimal Value

0.685345

Percentage

68.5345%

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Step-by-Step Solution: 9/29 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 8 = 232.

LCD(29, 8) = 232

Step 2

Convert to Equivalent Fractions with Common Denominator 232

Multiply the numerator and denominator of 9/29 by 8, and multiply the numerator and denominator of 3/8 by 29 so both fractions share the common base 232.

9 × 8/29 × 8 = 72/232 and 3 × 29/8 × 29 = 87/232

Step 3

Add the Numerators

Now add the numerators (72 + 87 = 159) and keep the common denominator 232 unchanged.

72 + 87/232 = 159/232

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 159 and 232 is 1, confirming that 159/232 cannot be reduced further—it is already in its simplest irreducible form.

159/232

Step 5

Decimal & Percentage Representation

Dividing the numerator 159 by denominator 232 produces a repeating decimal (approximately 0.685345, or 68.5345%).

159 ÷ 232 = 0.685345 (68.5345%)

Visual Representation

The diagram below illustrates 9/29 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`159/232`
Mixed Number Form	`159/232`
Decimal Form	`0.685345`
Percentage	`68.5345%`

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Frequently Asked Questions

What is 9/29 plus 3/8 as a fraction?

9/29 + 3/8 in simplest fraction form is 159/232.

What is 9/29 plus 3/8 as a decimal?

9/29 + 3/8 converted to a decimal is 0.685345.

What is 9/29 plus 3/8 as a percentage?

9/29 + 3/8 expressed as a percentage is 68.5345%.

Does 9/29 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.685345...) because the denominator contains prime factors other than 2 and 5.