What is 3/62 plus 2/13? (Answer: 163/806)

Exact Answer

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Problem: What is 3/62 plus 2/13?
Formula / Expression: 3/62 + 2/13
Final Answer: 163/806
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 62 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 62 × 13 = 806.
Working: LCD(62, 13) = 806

Step 2: Convert to Equivalent Fractions with Common Denominator 806
Multiply the numerator and denominator of 3/62 by 13, and multiply the numerator and denominator of 2/13 by 62 so both fractions share the common base 806.
Working: 3 × 13/62 × 13 = 39/806 and 2 × 62/13 × 62 = 124/806

Step 3: Add the Numerators
Now add the numerators (39 + 124 = 163) and keep the common denominator 806 unchanged.
Working: 39 + 124/806 = 163/806

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 163 and 806 is 1, confirming that 163/806 cannot be reduced further—it is already in its simplest irreducible form.
Working: 163/806

Step 5: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 806 produces a repeating decimal (approximately 0.202233, or 20.2233%).
Working: 163 ÷ 806 = 0.202233 (20.2233%)

Key Values:
- Simplified Fraction: 163/806
- Mixed Number Form: 163/806
- Decimal Value: 0.202233
- Percentage: 20.2233%

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Solved with FractionsCalc:
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3/62 + 2/13 = 163/806

Simplified Fraction

163/806

Mixed Number

Proper (163/806)

Decimal Value

0.202233

Percentage

20.2233%

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Step-by-Step Solution: 3/62 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 62 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 62 × 13 = 806.

LCD(62, 13) = 806

Step 2

Convert to Equivalent Fractions with Common Denominator 806

Multiply the numerator and denominator of 3/62 by 13, and multiply the numerator and denominator of 2/13 by 62 so both fractions share the common base 806.

3 × 13/62 × 13 = 39/806 and 2 × 62/13 × 62 = 124/806

Step 3

Add the Numerators

Now add the numerators (39 + 124 = 163) and keep the common denominator 806 unchanged.

39 + 124/806 = 163/806

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 163 and 806 is 1, confirming that 163/806 cannot be reduced further—it is already in its simplest irreducible form.

163/806

Step 5

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 806 produces a repeating decimal (approximately 0.202233, or 20.2233%).

163 ÷ 806 = 0.202233 (20.2233%)

Visual Representation

The diagram below illustrates 3/62 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/806`
Mixed Number Form	`163/806`
Decimal Form	`0.202233`
Percentage	`20.2233%`

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Frequently Asked Questions

What is 3/62 plus 2/13 as a fraction?

3/62 + 2/13 in simplest fraction form is 163/806.

What is 3/62 plus 2/13 as a decimal?

3/62 + 2/13 converted to a decimal is 0.202233.

What is 3/62 plus 2/13 as a percentage?

3/62 + 2/13 expressed as a percentage is 20.2233%.

Does 3/62 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.202233...) because the denominator contains prime factors other than 2 and 5.