What is 2/34 plus 2/10? (Answer: 22/85)

Exact Answer

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Problem: What is 2/34 plus 2/10?
Formula / Expression: 2/34 + 2/10
Final Answer: 22/85
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 170 (which is smaller than their product 34 × 10 = 340, keeping the calculation simpler).
Working: LCD(34, 10) = 170

Step 2: Convert to Equivalent Fractions with Common Denominator 170
Multiply the numerator and denominator of 2/34 by 5, and multiply the numerator and denominator of 2/10 by 17 so both fractions share the common base 170.
Working: 2 × 5/34 × 5 = 10/170 and 2 × 17/10 × 17 = 34/170

Step 3: Add the Numerators
Now add the numerators (10 + 34 = 44) and keep the common denominator 170 unchanged.
Working: 10 + 34/170 = 44/170

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 44 and 170, which is 2. Divide both the numerator and denominator by 2.
Working: 44 ÷ 2/170 ÷ 2 = 22/85

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 85 produces a repeating decimal (approximately 0.258824, or 25.8824%).
Working: 22 ÷ 85 = 0.258824 (25.8824%)

Key Values:
- Simplified Fraction: 22/85
- Mixed Number Form: 22/85
- Decimal Value: 0.258824
- Percentage: 25.8824%

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Solved with FractionsCalc:
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2/34 + 2/10 = 22/85

Simplified Fraction

22/85

Mixed Number

Proper (22/85)

Decimal Value

0.258824

Percentage

25.8824%

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Step-by-Step Solution: 2/34 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 170 (which is smaller than their product 34 × 10 = 340, keeping the calculation simpler).

LCD(34, 10) = 170

Step 2

Convert to Equivalent Fractions with Common Denominator 170

Multiply the numerator and denominator of 2/34 by 5, and multiply the numerator and denominator of 2/10 by 17 so both fractions share the common base 170.

2 × 5/34 × 5 = 10/170 and 2 × 17/10 × 17 = 34/170

Step 3

Add the Numerators

Now add the numerators (10 + 34 = 44) and keep the common denominator 170 unchanged.

10 + 34/170 = 44/170

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 44 and 170, which is 2. Divide both the numerator and denominator by 2.

44 ÷ 2/170 ÷ 2 = 22/85

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 85 produces a repeating decimal (approximately 0.258824, or 25.8824%).

22 ÷ 85 = 0.258824 (25.8824%)

Visual Representation

The diagram below illustrates 2/34 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/85`
Mixed Number Form	`22/85`
Decimal Form	`0.258824`
Percentage	`25.8824%`

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Frequently Asked Questions

What is 2/34 plus 2/10 as a fraction?

2/34 + 2/10 in simplest fraction form is 22/85.

What is 2/34 plus 2/10 as a decimal?

2/34 + 2/10 converted to a decimal is 0.258824.

What is 2/34 plus 2/10 as a percentage?

2/34 + 2/10 expressed as a percentage is 25.8824%.

Does 2/34 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.258824...) because the denominator contains prime factors other than 2 and 5.