What is 2/9 plus 10/17? (Answer: 124/153)

Exact Answer

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Problem: What is 2/9 plus 10/17?
Formula / Expression: 2/9 + 10/17
Final Answer: 124/153
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 17 = 153.
Working: LCD(9, 17) = 153

Step 2: Convert to Equivalent Fractions with Common Denominator 153
Multiply the numerator and denominator of 2/9 by 17, and multiply the numerator and denominator of 10/17 by 9 so both fractions share the common base 153.
Working: 2 × 17/9 × 17 = 34/153 and 10 × 9/17 × 9 = 90/153

Step 3: Add the Numerators
Now add the numerators (34 + 90 = 124) and keep the common denominator 153 unchanged.
Working: 34 + 90/153 = 124/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 124 and 153 is 1, confirming that 124/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 124/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 124 by denominator 153 produces a repeating decimal (approximately 0.810458, or 81.0458%).
Working: 124 ÷ 153 = 0.810458 (81.0458%)

Key Values:
- Simplified Fraction: 124/153
- Mixed Number Form: 124/153
- Decimal Value: 0.810458
- Percentage: 81.0458%

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Solved with FractionsCalc:
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2/9 + 10/17 = 124/153

Simplified Fraction

124/153

Mixed Number

Proper (124/153)

Decimal Value

0.810458

Percentage

81.0458%

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Step-by-Step Solution: 2/9 + 10/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 17 = 153.

LCD(9, 17) = 153

Step 2

Convert to Equivalent Fractions with Common Denominator 153

Multiply the numerator and denominator of 2/9 by 17, and multiply the numerator and denominator of 10/17 by 9 so both fractions share the common base 153.

2 × 17/9 × 17 = 34/153 and 10 × 9/17 × 9 = 90/153

Step 3

Add the Numerators

Now add the numerators (34 + 90 = 124) and keep the common denominator 153 unchanged.

34 + 90/153 = 124/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 124 and 153 is 1, confirming that 124/153 cannot be reduced further—it is already in its simplest irreducible form.

124/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 124 by denominator 153 produces a repeating decimal (approximately 0.810458, or 81.0458%).

124 ÷ 153 = 0.810458 (81.0458%)

Visual Representation

The diagram below illustrates 2/9 plus 10/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`124/153`
Mixed Number Form	`124/153`
Decimal Form	`0.810458`
Percentage	`81.0458%`

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Frequently Asked Questions

What is 2/9 plus 10/17 as a fraction?

2/9 + 10/17 in simplest fraction form is 124/153.

What is 2/9 plus 10/17 as a decimal?

2/9 + 10/17 converted to a decimal is 0.810458.

What is 2/9 plus 10/17 as a percentage?

2/9 + 10/17 expressed as a percentage is 81.0458%.

Does 2/9 plus 10/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.810458...) because the denominator contains prime factors other than 2 and 5.