What is 9/29 plus 3/9? (Answer: 56/87)

Exact Answer

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Problem: What is 9/29 plus 3/9?
Formula / Expression: 9/29 + 3/9
Final Answer: 56/87
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 9 = 261.
Working: LCD(29, 9) = 261

Step 2: Convert to Equivalent Fractions with Common Denominator 261
Multiply the numerator and denominator of 9/29 by 9, and multiply the numerator and denominator of 3/9 by 29 so both fractions share the common base 261.
Working: 9 × 9/29 × 9 = 81/261 and 3 × 29/9 × 29 = 87/261

Step 3: Add the Numerators
Now add the numerators (81 + 87 = 168) and keep the common denominator 261 unchanged.
Working: 81 + 87/261 = 168/261

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 168 and 261, which is 3. Divide both the numerator and denominator by 3.
Working: 168 ÷ 3/261 ÷ 3 = 56/87

Step 5: Decimal & Percentage Representation
Dividing the numerator 56 by denominator 87 produces a repeating decimal (approximately 0.643678, or 64.3678%).
Working: 56 ÷ 87 = 0.643678 (64.3678%)

Key Values:
- Simplified Fraction: 56/87
- Mixed Number Form: 56/87
- Decimal Value: 0.643678
- Percentage: 64.3678%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-29-plus-3-9/
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9/29 + 3/9 = 56/87

Simplified Fraction

56/87

Mixed Number

Proper (56/87)

Decimal Value

0.643678

Percentage

64.3678%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 9 = 261.

LCD(29, 9) = 261

Step 2

Convert to Equivalent Fractions with Common Denominator 261

Multiply the numerator and denominator of 9/29 by 9, and multiply the numerator and denominator of 3/9 by 29 so both fractions share the common base 261.

9 × 9/29 × 9 = 81/261 and 3 × 29/9 × 29 = 87/261

Step 3

Add the Numerators

Now add the numerators (81 + 87 = 168) and keep the common denominator 261 unchanged.

81 + 87/261 = 168/261

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 168 and 261, which is 3. Divide both the numerator and denominator by 3.

168 ÷ 3/261 ÷ 3 = 56/87

Step 5

Decimal & Percentage Representation

Dividing the numerator 56 by denominator 87 produces a repeating decimal (approximately 0.643678, or 64.3678%).

56 ÷ 87 = 0.643678 (64.3678%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`56/87`
Mixed Number Form	`56/87`
Decimal Form	`0.643678`
Percentage	`64.3678%`

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Frequently Asked Questions

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

9/29 + 3/9 in simplest fraction form is 56/87.

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

9/29 + 3/9 converted to a decimal is 0.643678.

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

9/29 + 3/9 expressed as a percentage is 64.3678%.

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

It results in a repeating decimal (approximately 0.643678...) because the denominator contains prime factors other than 2 and 5.