What is 2/31 plus 2/5? (Answer: 72/155)

Exact Answer

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Problem: What is 2/31 plus 2/5?
Formula / Expression: 2/31 + 2/5
Final Answer: 72/155
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 5 = 155.
Working: LCD(31, 5) = 155

Step 2: Convert to Equivalent Fractions with Common Denominator 155
Multiply the numerator and denominator of 2/31 by 5, and multiply the numerator and denominator of 2/5 by 31 so both fractions share the common base 155.
Working: 2 × 5/31 × 5 = 10/155 and 2 × 31/5 × 31 = 62/155

Step 3: Add the Numerators
Now add the numerators (10 + 62 = 72) and keep the common denominator 155 unchanged.
Working: 10 + 62/155 = 72/155

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 72 and 155 is 1, confirming that 72/155 cannot be reduced further—it is already in its simplest irreducible form.
Working: 72/155

Step 5: Decimal & Percentage Representation
Dividing the numerator 72 by denominator 155 produces a repeating decimal (approximately 0.464516, or 46.4516%).
Working: 72 ÷ 155 = 0.464516 (46.4516%)

Key Values:
- Simplified Fraction: 72/155
- Mixed Number Form: 72/155
- Decimal Value: 0.464516
- Percentage: 46.4516%

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Solved with FractionsCalc:
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2/31 + 2/5 = 72/155

Simplified Fraction

72/155

Mixed Number

Proper (72/155)

Decimal Value

0.464516

Percentage

46.4516%

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Step-by-Step Solution: 2/31 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 5 = 155.

LCD(31, 5) = 155

Step 2

Convert to Equivalent Fractions with Common Denominator 155

Multiply the numerator and denominator of 2/31 by 5, and multiply the numerator and denominator of 2/5 by 31 so both fractions share the common base 155.

2 × 5/31 × 5 = 10/155 and 2 × 31/5 × 31 = 62/155

Step 3

Add the Numerators

Now add the numerators (10 + 62 = 72) and keep the common denominator 155 unchanged.

10 + 62/155 = 72/155

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 72 and 155 is 1, confirming that 72/155 cannot be reduced further—it is already in its simplest irreducible form.

72/155

Step 5

Decimal & Percentage Representation

Dividing the numerator 72 by denominator 155 produces a repeating decimal (approximately 0.464516, or 46.4516%).

72 ÷ 155 = 0.464516 (46.4516%)

Visual Representation

The diagram below illustrates 2/31 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`72/155`
Mixed Number Form	`72/155`
Decimal Form	`0.464516`
Percentage	`46.4516%`

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Frequently Asked Questions

What is 2/31 plus 2/5 as a fraction?

2/31 + 2/5 in simplest fraction form is 72/155.

What is 2/31 plus 2/5 as a decimal?

2/31 + 2/5 converted to a decimal is 0.464516.

What is 2/31 plus 2/5 as a percentage?

2/31 + 2/5 expressed as a percentage is 46.4516%.

Does 2/31 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.464516...) because the denominator contains prime factors other than 2 and 5.