What is 2/34 plus 2/8? (Answer: 21/68)

Exact Answer

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Problem: What is 2/34 plus 2/8?
Formula / Expression: 2/34 + 2/8
Final Answer: 21/68
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 136 (which is smaller than their product 34 × 8 = 272, keeping the calculation simpler).
Working: LCD(34, 8) = 136

Step 2: Convert to Equivalent Fractions with Common Denominator 136
Multiply the numerator and denominator of 2/34 by 4, and multiply the numerator and denominator of 2/8 by 17 so both fractions share the common base 136.
Working: 2 × 4/34 × 4 = 8/136 and 2 × 17/8 × 17 = 34/136

Step 3: Add the Numerators
Now add the numerators (8 + 34 = 42) and keep the common denominator 136 unchanged.
Working: 8 + 34/136 = 42/136

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 136, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/136 ÷ 2 = 21/68

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 68 produces a repeating decimal (approximately 0.308824, or 30.8824%).
Working: 21 ÷ 68 = 0.308824 (30.8824%)

Key Values:
- Simplified Fraction: 21/68
- Mixed Number Form: 21/68
- Decimal Value: 0.308824
- Percentage: 30.8824%

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Solved with FractionsCalc:
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2/34 + 2/8 = 21/68

Simplified Fraction

21/68

Mixed Number

Proper (21/68)

Decimal Value

0.308824

Percentage

30.8824%

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Step-by-Step Solution: 2/34 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 136 (which is smaller than their product 34 × 8 = 272, keeping the calculation simpler).

LCD(34, 8) = 136

Step 2

Convert to Equivalent Fractions with Common Denominator 136

Multiply the numerator and denominator of 2/34 by 4, and multiply the numerator and denominator of 2/8 by 17 so both fractions share the common base 136.

2 × 4/34 × 4 = 8/136 and 2 × 17/8 × 17 = 34/136

Step 3

Add the Numerators

Now add the numerators (8 + 34 = 42) and keep the common denominator 136 unchanged.

8 + 34/136 = 42/136

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 136, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/136 ÷ 2 = 21/68

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 68 produces a repeating decimal (approximately 0.308824, or 30.8824%).

21 ÷ 68 = 0.308824 (30.8824%)

Visual Representation

The diagram below illustrates 2/34 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/68`
Mixed Number Form	`21/68`
Decimal Form	`0.308824`
Percentage	`30.8824%`

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Frequently Asked Questions

What is 2/34 plus 2/8 as a fraction?

2/34 + 2/8 in simplest fraction form is 21/68.

What is 2/34 plus 2/8 as a decimal?

2/34 + 2/8 converted to a decimal is 0.308824.

What is 2/34 plus 2/8 as a percentage?

2/34 + 2/8 expressed as a percentage is 30.8824%.

Does 2/34 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.308824...) because the denominator contains prime factors other than 2 and 5.