What is 3/34 plus 2/7? (Answer: 89/238)

Exact Answer

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Problem: What is 3/34 plus 2/7?
Formula / Expression: 3/34 + 2/7
Final Answer: 89/238
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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 3/34 by 7, and multiply the numerator and denominator of 2/7 by 34 so both fractions share the common base 238.
Working: 3 × 7/34 × 7 = 21/238 and 2 × 34/7 × 34 = 68/238

Step 3: Add the Numerators
Now add the numerators (21 + 68 = 89) and keep the common denominator 238 unchanged.
Working: 21 + 68/238 = 89/238

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 238 is 1, confirming that 89/238 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/238

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 238 produces a repeating decimal (approximately 0.37395, or 37.395%).
Working: 89 ÷ 238 = 0.37395 (37.395%)

Key Values:
- Simplified Fraction: 89/238
- Mixed Number Form: 89/238
- Decimal Value: 0.37395
- Percentage: 37.395%

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Solved with FractionsCalc:
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3/34 + 2/7 = 89/238

Simplified Fraction

89/238

Mixed Number

Proper (89/238)

Decimal Value

0.37395

Percentage

37.395%

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Step-by-Step Solution: 3/34 + 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 3/34 by 7, and multiply the numerator and denominator of 2/7 by 34 so both fractions share the common base 238.

3 × 7/34 × 7 = 21/238 and 2 × 34/7 × 34 = 68/238

Step 3

Add the Numerators

Now add the numerators (21 + 68 = 89) and keep the common denominator 238 unchanged.

21 + 68/238 = 89/238

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 238 is 1, confirming that 89/238 cannot be reduced further—it is already in its simplest irreducible form.

89/238

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 238 produces a repeating decimal (approximately 0.37395, or 37.395%).

89 ÷ 238 = 0.37395 (37.395%)

Visual Representation

The diagram below illustrates 3/34 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/238`
Mixed Number Form	`89/238`
Decimal Form	`0.37395`
Percentage	`37.395%`

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Frequently Asked Questions

What is 3/34 plus 2/7 as a fraction?

3/34 + 2/7 in simplest fraction form is 89/238.

What is 3/34 plus 2/7 as a decimal?

3/34 + 2/7 converted to a decimal is 0.37395.

What is 3/34 plus 2/7 as a percentage?

3/34 + 2/7 expressed as a percentage is 37.395%.

Does 3/34 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.37395...) because the denominator contains prime factors other than 2 and 5.