What is 7/34 plus 2/9? (Answer: 131/306)

Exact Answer

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Problem: What is 7/34 plus 2/9?
Formula / Expression: 7/34 + 2/9
Final Answer: 131/306
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 9 = 306.
Working: LCD(34, 9) = 306

Step 2: Convert to Equivalent Fractions with Common Denominator 306
Multiply the numerator and denominator of 7/34 by 9, and multiply the numerator and denominator of 2/9 by 34 so both fractions share the common base 306.
Working: 7 × 9/34 × 9 = 63/306 and 2 × 34/9 × 34 = 68/306

Step 3: Add the Numerators
Now add the numerators (63 + 68 = 131) and keep the common denominator 306 unchanged.
Working: 63 + 68/306 = 131/306

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 131 and 306 is 1, confirming that 131/306 cannot be reduced further—it is already in its simplest irreducible form.
Working: 131/306

Step 5: Decimal & Percentage Representation
Dividing the numerator 131 by denominator 306 produces a repeating decimal (approximately 0.428105, or 42.8105%).
Working: 131 ÷ 306 = 0.428105 (42.8105%)

Key Values:
- Simplified Fraction: 131/306
- Mixed Number Form: 131/306
- Decimal Value: 0.428105
- Percentage: 42.8105%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-34-plus-2-9/
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7/34 + 2/9 = 131/306

Simplified Fraction

131/306

Mixed Number

Proper (131/306)

Decimal Value

0.428105

Percentage

42.8105%

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Step-by-Step Solution: 7/34 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 9 = 306.

LCD(34, 9) = 306

Step 2

Convert to Equivalent Fractions with Common Denominator 306

Multiply the numerator and denominator of 7/34 by 9, and multiply the numerator and denominator of 2/9 by 34 so both fractions share the common base 306.

7 × 9/34 × 9 = 63/306 and 2 × 34/9 × 34 = 68/306

Step 3

Add the Numerators

Now add the numerators (63 + 68 = 131) and keep the common denominator 306 unchanged.

63 + 68/306 = 131/306

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 131 and 306 is 1, confirming that 131/306 cannot be reduced further—it is already in its simplest irreducible form.

131/306

Step 5

Decimal & Percentage Representation

Dividing the numerator 131 by denominator 306 produces a repeating decimal (approximately 0.428105, or 42.8105%).

131 ÷ 306 = 0.428105 (42.8105%)

Visual Representation

The diagram below illustrates 7/34 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`131/306`
Mixed Number Form	`131/306`
Decimal Form	`0.428105`
Percentage	`42.8105%`

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Frequently Asked Questions

What is 7/34 plus 2/9 as a fraction?

7/34 + 2/9 in simplest fraction form is 131/306.

What is 7/34 plus 2/9 as a decimal?

7/34 + 2/9 converted to a decimal is 0.428105.

What is 7/34 plus 2/9 as a percentage?

7/34 + 2/9 expressed as a percentage is 42.8105%.

Does 7/34 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.428105...) because the denominator contains prime factors other than 2 and 5.