What is 2/68 plus 2/13? (Answer: 81/442)

Exact Answer

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Problem: What is 2/68 plus 2/13?
Formula / Expression: 2/68 + 2/13
Final Answer: 81/442
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 68 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 68 × 13 = 884.
Working: LCD(68, 13) = 884

Step 2: Convert to Equivalent Fractions with Common Denominator 884
Multiply the numerator and denominator of 2/68 by 13, and multiply the numerator and denominator of 2/13 by 68 so both fractions share the common base 884.
Working: 2 × 13/68 × 13 = 26/884 and 2 × 68/13 × 68 = 136/884

Step 3: Add the Numerators
Now add the numerators (26 + 136 = 162) and keep the common denominator 884 unchanged.
Working: 26 + 136/884 = 162/884

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 162 and 884, which is 2. Divide both the numerator and denominator by 2.
Working: 162 ÷ 2/884 ÷ 2 = 81/442

Step 5: Decimal & Percentage Representation
Dividing the numerator 81 by denominator 442 produces a repeating decimal (approximately 0.183258, or 18.3258%).
Working: 81 ÷ 442 = 0.183258 (18.3258%)

Key Values:
- Simplified Fraction: 81/442
- Mixed Number Form: 81/442
- Decimal Value: 0.183258
- Percentage: 18.3258%

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Solved with FractionsCalc:
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2/68 + 2/13 = 81/442

Simplified Fraction

81/442

Mixed Number

Proper (81/442)

Decimal Value

0.183258

Percentage

18.3258%

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Step-by-Step Solution: 2/68 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 68 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 68 × 13 = 884.

LCD(68, 13) = 884

Step 2

Convert to Equivalent Fractions with Common Denominator 884

Multiply the numerator and denominator of 2/68 by 13, and multiply the numerator and denominator of 2/13 by 68 so both fractions share the common base 884.

2 × 13/68 × 13 = 26/884 and 2 × 68/13 × 68 = 136/884

Step 3

Add the Numerators

Now add the numerators (26 + 136 = 162) and keep the common denominator 884 unchanged.

26 + 136/884 = 162/884

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 162 and 884, which is 2. Divide both the numerator and denominator by 2.

162 ÷ 2/884 ÷ 2 = 81/442

Step 5

Decimal & Percentage Representation

Dividing the numerator 81 by denominator 442 produces a repeating decimal (approximately 0.183258, or 18.3258%).

81 ÷ 442 = 0.183258 (18.3258%)

Visual Representation

The diagram below illustrates 2/68 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`81/442`
Mixed Number Form	`81/442`
Decimal Form	`0.183258`
Percentage	`18.3258%`

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Frequently Asked Questions

What is 2/68 plus 2/13 as a fraction?

2/68 + 2/13 in simplest fraction form is 81/442.

What is 2/68 plus 2/13 as a decimal?

2/68 + 2/13 converted to a decimal is 0.183258.

What is 2/68 plus 2/13 as a percentage?

2/68 + 2/13 expressed as a percentage is 18.3258%.

Does 2/68 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.183258...) because the denominator contains prime factors other than 2 and 5.