What is 2/17 plus 2/10? (Answer: 27/85)

Exact Answer

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Problem: What is 2/17 plus 2/10?
Formula / Expression: 2/17 + 2/10
Final Answer: 27/85
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 10 = 170.
Working: LCD(17, 10) = 170

Step 2: Convert to Equivalent Fractions with Common Denominator 170
Multiply the numerator and denominator of 2/17 by 10, and multiply the numerator and denominator of 2/10 by 17 so both fractions share the common base 170.
Working: 2 × 10/17 × 10 = 20/170 and 2 × 17/10 × 17 = 34/170

Step 3: Add the Numerators
Now add the numerators (20 + 34 = 54) and keep the common denominator 170 unchanged.
Working: 20 + 34/170 = 54/170

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 54 and 170, which is 2. Divide both the numerator and denominator by 2.
Working: 54 ÷ 2/170 ÷ 2 = 27/85

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 85 produces a repeating decimal (approximately 0.317647, or 31.7647%).
Working: 27 ÷ 85 = 0.317647 (31.7647%)

Key Values:
- Simplified Fraction: 27/85
- Mixed Number Form: 27/85
- Decimal Value: 0.317647
- Percentage: 31.7647%

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Solved with FractionsCalc:
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2/17 + 2/10 = 27/85

Simplified Fraction

27/85

Mixed Number

Proper (27/85)

Decimal Value

0.317647

Percentage

31.7647%

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Step-by-Step Solution: 2/17 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 10 = 170.

LCD(17, 10) = 170

Step 2

Convert to Equivalent Fractions with Common Denominator 170

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

2 × 10/17 × 10 = 20/170 and 2 × 17/10 × 17 = 34/170

Step 3

Add the Numerators

Now add the numerators (20 + 34 = 54) and keep the common denominator 170 unchanged.

20 + 34/170 = 54/170

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 54 and 170, which is 2. Divide both the numerator and denominator by 2.

54 ÷ 2/170 ÷ 2 = 27/85

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 85 produces a repeating decimal (approximately 0.317647, or 31.7647%).

27 ÷ 85 = 0.317647 (31.7647%)

Visual Representation

The diagram below illustrates 2/17 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/85`
Mixed Number Form	`27/85`
Decimal Form	`0.317647`
Percentage	`31.7647%`

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Frequently Asked Questions

What is 2/17 plus 2/10 as a fraction?

2/17 + 2/10 in simplest fraction form is 27/85.

What is 2/17 plus 2/10 as a decimal?

2/17 + 2/10 converted to a decimal is 0.317647.

What is 2/17 plus 2/10 as a percentage?

2/17 + 2/10 expressed as a percentage is 31.7647%.

Does 2/17 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.317647...) because the denominator contains prime factors other than 2 and 5.