What is 2/9 plus 8/34? (Answer: 70/153)

Exact Answer

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Problem: What is 2/9 plus 8/34?
Formula / Expression: 2/9 + 8/34
Final Answer: 70/153
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 306
Multiply the numerator and denominator of 2/9 by 34, and multiply the numerator and denominator of 8/34 by 9 so both fractions share the common base 306.
Working: 2 × 34/9 × 34 = 68/306 and 8 × 9/34 × 9 = 72/306

Step 3: Add the Numerators
Now add the numerators (68 + 72 = 140) and keep the common denominator 306 unchanged.
Working: 68 + 72/306 = 140/306

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 306, which is 2. Divide both the numerator and denominator by 2.
Working: 140 ÷ 2/306 ÷ 2 = 70/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 70 by denominator 153 produces a repeating decimal (approximately 0.457516, or 45.7516%).
Working: 70 ÷ 153 = 0.457516 (45.7516%)

Key Values:
- Simplified Fraction: 70/153
- Mixed Number Form: 70/153
- Decimal Value: 0.457516
- Percentage: 45.7516%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-8-34/
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2/9 + 8/34 = 70/153

Simplified Fraction

70/153

Mixed Number

Proper (70/153)

Decimal Value

0.457516

Percentage

45.7516%

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Step-by-Step Solution: 2/9 + 8/34

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 34) = 306

Step 2

Convert to Equivalent Fractions with Common Denominator 306

Multiply the numerator and denominator of 2/9 by 34, and multiply the numerator and denominator of 8/34 by 9 so both fractions share the common base 306.

2 × 34/9 × 34 = 68/306 and 8 × 9/34 × 9 = 72/306

Step 3

Add the Numerators

Now add the numerators (68 + 72 = 140) and keep the common denominator 306 unchanged.

68 + 72/306 = 140/306

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 306, which is 2. Divide both the numerator and denominator by 2.

140 ÷ 2/306 ÷ 2 = 70/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 70 by denominator 153 produces a repeating decimal (approximately 0.457516, or 45.7516%).

70 ÷ 153 = 0.457516 (45.7516%)

Visual Representation

The diagram below illustrates 2/9 plus 8/34 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`70/153`
Mixed Number Form	`70/153`
Decimal Form	`0.457516`
Percentage	`45.7516%`

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Frequently Asked Questions

What is 2/9 plus 8/34 as a fraction?

2/9 + 8/34 in simplest fraction form is 70/153.

What is 2/9 plus 8/34 as a decimal?

2/9 + 8/34 converted to a decimal is 0.457516.

What is 2/9 plus 8/34 as a percentage?

2/9 + 8/34 expressed as a percentage is 45.7516%.

Does 2/9 plus 8/34 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.457516...) because the denominator contains prime factors other than 2 and 5.