What is 8/34 plus 2/7? (Answer: 62/119)

Exact Answer

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Problem: What is 8/34 plus 2/7?
Formula / Expression: 8/34 + 2/7
Final Answer: 62/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 7 = 238.
Working: LCD(34, 7) = 238

Step 2: Convert to Equivalent Fractions with Common Denominator 238
Multiply the numerator and denominator of 8/34 by 7, and multiply the numerator and denominator of 2/7 by 34 so both fractions share the common base 238.
Working: 8 × 7/34 × 7 = 56/238 and 2 × 34/7 × 34 = 68/238

Step 3: Add the Numerators
Now add the numerators (56 + 68 = 124) and keep the common denominator 238 unchanged.
Working: 56 + 68/238 = 124/238

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 124 and 238, which is 2. Divide both the numerator and denominator by 2.
Working: 124 ÷ 2/238 ÷ 2 = 62/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 62 by denominator 119 produces a repeating decimal (approximately 0.521008, or 52.1008%).
Working: 62 ÷ 119 = 0.521008 (52.1008%)

Key Values:
- Simplified Fraction: 62/119
- Mixed Number Form: 62/119
- Decimal Value: 0.521008
- Percentage: 52.1008%

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Solved with FractionsCalc:
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8/34 + 2/7 = 62/119

Simplified Fraction

62/119

Mixed Number

Proper (62/119)

Decimal Value

0.521008

Percentage

52.1008%

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Step-by-Step Solution: 8/34 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 7 = 238.

LCD(34, 7) = 238

Step 2

Convert to Equivalent Fractions with Common Denominator 238

Multiply the numerator and denominator of 8/34 by 7, and multiply the numerator and denominator of 2/7 by 34 so both fractions share the common base 238.

8 × 7/34 × 7 = 56/238 and 2 × 34/7 × 34 = 68/238

Step 3

Add the Numerators

Now add the numerators (56 + 68 = 124) and keep the common denominator 238 unchanged.

56 + 68/238 = 124/238

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 124 and 238, which is 2. Divide both the numerator and denominator by 2.

124 ÷ 2/238 ÷ 2 = 62/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 62 by denominator 119 produces a repeating decimal (approximately 0.521008, or 52.1008%).

62 ÷ 119 = 0.521008 (52.1008%)

Visual Representation

The diagram below illustrates 8/34 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`62/119`
Mixed Number Form	`62/119`
Decimal Form	`0.521008`
Percentage	`52.1008%`

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Frequently Asked Questions

What is 8/34 plus 2/7 as a fraction?

8/34 + 2/7 in simplest fraction form is 62/119.

What is 8/34 plus 2/7 as a decimal?

8/34 + 2/7 converted to a decimal is 0.521008.

What is 8/34 plus 2/7 as a percentage?

8/34 + 2/7 expressed as a percentage is 52.1008%.

Does 8/34 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.521008...) because the denominator contains prime factors other than 2 and 5.