What is 9/29 plus 2/3? (Answer: 85/87)

Exact Answer

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Problem: What is 9/29 plus 2/3?
Formula / Expression: 9/29 + 2/3
Final Answer: 85/87
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 3 = 87.
Working: LCD(29, 3) = 87

Step 2: Convert to Equivalent Fractions with Common Denominator 87
Multiply the numerator and denominator of 9/29 by 3, and multiply the numerator and denominator of 2/3 by 29 so both fractions share the common base 87.
Working: 9 × 3/29 × 3 = 27/87 and 2 × 29/3 × 29 = 58/87

Step 3: Add the Numerators
Now add the numerators (27 + 58 = 85) and keep the common denominator 87 unchanged.
Working: 27 + 58/87 = 85/87

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 87 is 1, confirming that 85/87 cannot be reduced further—it is already in its simplest irreducible form.
Working: 85/87

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 87 produces a repeating decimal (approximately 0.977011, or 97.7011%).
Working: 85 ÷ 87 = 0.977011 (97.7011%)

Key Values:
- Simplified Fraction: 85/87
- Mixed Number Form: 85/87
- Decimal Value: 0.977011
- Percentage: 97.7011%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-29-plus-2-3/
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9/29 + 2/3 = 85/87

Simplified Fraction

85/87

Mixed Number

Proper (85/87)

Decimal Value

0.977011

Percentage

97.7011%

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Step-by-Step Solution: 9/29 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 3 = 87.

LCD(29, 3) = 87

Step 2

Convert to Equivalent Fractions with Common Denominator 87

Multiply the numerator and denominator of 9/29 by 3, and multiply the numerator and denominator of 2/3 by 29 so both fractions share the common base 87.

9 × 3/29 × 3 = 27/87 and 2 × 29/3 × 29 = 58/87

Step 3

Add the Numerators

Now add the numerators (27 + 58 = 85) and keep the common denominator 87 unchanged.

27 + 58/87 = 85/87

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 85 and 87 is 1, confirming that 85/87 cannot be reduced further—it is already in its simplest irreducible form.

85/87

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 87 produces a repeating decimal (approximately 0.977011, or 97.7011%).

85 ÷ 87 = 0.977011 (97.7011%)

Visual Representation

The diagram below illustrates 9/29 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/87`
Mixed Number Form	`85/87`
Decimal Form	`0.977011`
Percentage	`97.7011%`

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Frequently Asked Questions

What is 9/29 plus 2/3 as a fraction?

9/29 + 2/3 in simplest fraction form is 85/87.

What is 9/29 plus 2/3 as a decimal?

9/29 + 2/3 converted to a decimal is 0.977011.

What is 9/29 plus 2/3 as a percentage?

9/29 + 2/3 expressed as a percentage is 97.7011%.

Does 9/29 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.977011...) because the denominator contains prime factors other than 2 and 5.