What is 2/29 plus 2/5? (Answer: 68/145)

Exact Answer

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Problem: What is 2/29 plus 2/5?
Formula / Expression: 2/29 + 2/5
Final Answer: 68/145
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 5 = 145.
Working: LCD(29, 5) = 145

Step 2: Convert to Equivalent Fractions with Common Denominator 145
Multiply the numerator and denominator of 2/29 by 5, and multiply the numerator and denominator of 2/5 by 29 so both fractions share the common base 145.
Working: 2 × 5/29 × 5 = 10/145 and 2 × 29/5 × 29 = 58/145

Step 3: Add the Numerators
Now add the numerators (10 + 58 = 68) and keep the common denominator 145 unchanged.
Working: 10 + 58/145 = 68/145

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 68 and 145 is 1, confirming that 68/145 cannot be reduced further—it is already in its simplest irreducible form.
Working: 68/145

Step 5: Decimal & Percentage Representation
Dividing the numerator 68 by denominator 145 produces a repeating decimal (approximately 0.468966, or 46.8966%).
Working: 68 ÷ 145 = 0.468966 (46.8966%)

Key Values:
- Simplified Fraction: 68/145
- Mixed Number Form: 68/145
- Decimal Value: 0.468966
- Percentage: 46.8966%

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2/29 + 2/5 = 68/145

Simplified Fraction

68/145

Mixed Number

Proper (68/145)

Decimal Value

0.468966

Percentage

46.8966%

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Step-by-Step Solution: 2/29 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 5 = 145.

LCD(29, 5) = 145

Step 2

Convert to Equivalent Fractions with Common Denominator 145

Multiply the numerator and denominator of 2/29 by 5, and multiply the numerator and denominator of 2/5 by 29 so both fractions share the common base 145.

2 × 5/29 × 5 = 10/145 and 2 × 29/5 × 29 = 58/145

Step 3

Add the Numerators

Now add the numerators (10 + 58 = 68) and keep the common denominator 145 unchanged.

10 + 58/145 = 68/145

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 68 and 145 is 1, confirming that 68/145 cannot be reduced further—it is already in its simplest irreducible form.

68/145

Step 5

Decimal & Percentage Representation

Dividing the numerator 68 by denominator 145 produces a repeating decimal (approximately 0.468966, or 46.8966%).

68 ÷ 145 = 0.468966 (46.8966%)

Visual Representation

The diagram below illustrates 2/29 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`68/145`
Mixed Number Form	`68/145`
Decimal Form	`0.468966`
Percentage	`46.8966%`

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Frequently Asked Questions

What is 2/29 plus 2/5 as a fraction?

2/29 + 2/5 in simplest fraction form is 68/145.

What is 2/29 plus 2/5 as a decimal?

2/29 + 2/5 converted to a decimal is 0.468966.

What is 2/29 plus 2/5 as a percentage?

2/29 + 2/5 expressed as a percentage is 46.8966%.

Does 2/29 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.468966...) because the denominator contains prime factors other than 2 and 5.