What is 3/68 plus 2/13? (Answer: 175/884)

Exact Answer

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Problem: What is 3/68 plus 2/13?
Formula / Expression: 3/68 + 2/13
Final Answer: 175/884
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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 3/68 by 13, and multiply the numerator and denominator of 2/13 by 68 so both fractions share the common base 884.
Working: 3 × 13/68 × 13 = 39/884 and 2 × 68/13 × 68 = 136/884

Step 3: Add the Numerators
Now add the numerators (39 + 136 = 175) and keep the common denominator 884 unchanged.
Working: 39 + 136/884 = 175/884

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 175 and 884 is 1, confirming that 175/884 cannot be reduced further—it is already in its simplest irreducible form.
Working: 175/884

Step 5: Decimal & Percentage Representation
Dividing the numerator 175 by denominator 884 produces a repeating decimal (approximately 0.197964, or 19.7964%).
Working: 175 ÷ 884 = 0.197964 (19.7964%)

Key Values:
- Simplified Fraction: 175/884
- Mixed Number Form: 175/884
- Decimal Value: 0.197964
- Percentage: 19.7964%

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Solved with FractionsCalc:
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3/68 + 2/13 = 175/884

Simplified Fraction

175/884

Mixed Number

Proper (175/884)

Decimal Value

0.197964

Percentage

19.7964%

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Step-by-Step Solution: 3/68 + 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 3/68 by 13, and multiply the numerator and denominator of 2/13 by 68 so both fractions share the common base 884.

3 × 13/68 × 13 = 39/884 and 2 × 68/13 × 68 = 136/884

Step 3

Add the Numerators

Now add the numerators (39 + 136 = 175) and keep the common denominator 884 unchanged.

39 + 136/884 = 175/884

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 175 and 884 is 1, confirming that 175/884 cannot be reduced further—it is already in its simplest irreducible form.

175/884

Step 5

Decimal & Percentage Representation

Dividing the numerator 175 by denominator 884 produces a repeating decimal (approximately 0.197964, or 19.7964%).

175 ÷ 884 = 0.197964 (19.7964%)

Visual Representation

The diagram below illustrates 3/68 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`175/884`
Mixed Number Form	`175/884`
Decimal Form	`0.197964`
Percentage	`19.7964%`

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Frequently Asked Questions

What is 3/68 plus 2/13 as a fraction?

3/68 + 2/13 in simplest fraction form is 175/884.

What is 3/68 plus 2/13 as a decimal?

3/68 + 2/13 converted to a decimal is 0.197964.

What is 3/68 plus 2/13 as a percentage?

3/68 + 2/13 expressed as a percentage is 19.7964%.

Does 3/68 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.197964...) because the denominator contains prime factors other than 2 and 5.