What is 3/67 plus 2/13? (Answer: 173/871)

Exact Answer

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Problem: What is 3/67 plus 2/13?
Formula / Expression: 3/67 + 2/13
Final Answer: 173/871
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 67 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 67 × 13 = 871.
Working: LCD(67, 13) = 871

Step 2: Convert to Equivalent Fractions with Common Denominator 871
Multiply the numerator and denominator of 3/67 by 13, and multiply the numerator and denominator of 2/13 by 67 so both fractions share the common base 871.
Working: 3 × 13/67 × 13 = 39/871 and 2 × 67/13 × 67 = 134/871

Step 3: Add the Numerators
Now add the numerators (39 + 134 = 173) and keep the common denominator 871 unchanged.
Working: 39 + 134/871 = 173/871

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 173 and 871 is 1, confirming that 173/871 cannot be reduced further—it is already in its simplest irreducible form.
Working: 173/871

Step 5: Decimal & Percentage Representation
Dividing the numerator 173 by denominator 871 produces a repeating decimal (approximately 0.198622, or 19.8622%).
Working: 173 ÷ 871 = 0.198622 (19.8622%)

Key Values:
- Simplified Fraction: 173/871
- Mixed Number Form: 173/871
- Decimal Value: 0.198622
- Percentage: 19.8622%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-67-plus-2-13/
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3/67 + 2/13 = 173/871

Simplified Fraction

173/871

Mixed Number

Proper (173/871)

Decimal Value

0.198622

Percentage

19.8622%

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Step-by-Step Solution: 3/67 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 67 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 67 × 13 = 871.

LCD(67, 13) = 871

Step 2

Convert to Equivalent Fractions with Common Denominator 871

Multiply the numerator and denominator of 3/67 by 13, and multiply the numerator and denominator of 2/13 by 67 so both fractions share the common base 871.

3 × 13/67 × 13 = 39/871 and 2 × 67/13 × 67 = 134/871

Step 3

Add the Numerators

Now add the numerators (39 + 134 = 173) and keep the common denominator 871 unchanged.

39 + 134/871 = 173/871

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 173 and 871 is 1, confirming that 173/871 cannot be reduced further—it is already in its simplest irreducible form.

173/871

Step 5

Decimal & Percentage Representation

Dividing the numerator 173 by denominator 871 produces a repeating decimal (approximately 0.198622, or 19.8622%).

173 ÷ 871 = 0.198622 (19.8622%)

Visual Representation

The diagram below illustrates 3/67 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`173/871`
Mixed Number Form	`173/871`
Decimal Form	`0.198622`
Percentage	`19.8622%`

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Frequently Asked Questions

What is 3/67 plus 2/13 as a fraction?

3/67 + 2/13 in simplest fraction form is 173/871.

What is 3/67 plus 2/13 as a decimal?

3/67 + 2/13 converted to a decimal is 0.198622.

What is 3/67 plus 2/13 as a percentage?

3/67 + 2/13 expressed as a percentage is 19.8622%.

Does 3/67 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.198622...) because the denominator contains prime factors other than 2 and 5.