What is 3/7 plus 9/17? (Answer: 114/119)

Exact Answer

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Problem: What is 3/7 plus 9/17?
Formula / Expression: 3/7 + 9/17
Final Answer: 114/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 17 = 119.
Working: LCD(7, 17) = 119

Step 2: Convert to Equivalent Fractions with Common Denominator 119
Multiply the numerator and denominator of 3/7 by 17, and multiply the numerator and denominator of 9/17 by 7 so both fractions share the common base 119.
Working: 3 × 17/7 × 17 = 51/119 and 9 × 7/17 × 7 = 63/119

Step 3: Add the Numerators
Now add the numerators (51 + 63 = 114) and keep the common denominator 119 unchanged.
Working: 51 + 63/119 = 114/119

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 114 and 119 is 1, confirming that 114/119 cannot be reduced further—it is already in its simplest irreducible form.
Working: 114/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 114 by denominator 119 produces a repeating decimal (approximately 0.957983, or 95.7983%).
Working: 114 ÷ 119 = 0.957983 (95.7983%)

Key Values:
- Simplified Fraction: 114/119
- Mixed Number Form: 114/119
- Decimal Value: 0.957983
- Percentage: 95.7983%

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Solved with FractionsCalc:
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3/7 + 9/17 = 114/119

Simplified Fraction

114/119

Mixed Number

Proper (114/119)

Decimal Value

0.957983

Percentage

95.7983%

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Step-by-Step Solution: 3/7 + 9/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 17 = 119.

LCD(7, 17) = 119

Step 2

Convert to Equivalent Fractions with Common Denominator 119

Multiply the numerator and denominator of 3/7 by 17, and multiply the numerator and denominator of 9/17 by 7 so both fractions share the common base 119.

3 × 17/7 × 17 = 51/119 and 9 × 7/17 × 7 = 63/119

Step 3

Add the Numerators

Now add the numerators (51 + 63 = 114) and keep the common denominator 119 unchanged.

51 + 63/119 = 114/119

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 114 and 119 is 1, confirming that 114/119 cannot be reduced further—it is already in its simplest irreducible form.

114/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 114 by denominator 119 produces a repeating decimal (approximately 0.957983, or 95.7983%).

114 ÷ 119 = 0.957983 (95.7983%)

Visual Representation

The diagram below illustrates 3/7 plus 9/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`114/119`
Mixed Number Form	`114/119`
Decimal Form	`0.957983`
Percentage	`95.7983%`

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Frequently Asked Questions

What is 3/7 plus 9/17 as a fraction?

3/7 + 9/17 in simplest fraction form is 114/119.

What is 3/7 plus 9/17 as a decimal?

3/7 + 9/17 converted to a decimal is 0.957983.

What is 3/7 plus 9/17 as a percentage?

3/7 + 9/17 expressed as a percentage is 95.7983%.

Does 3/7 plus 9/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.957983...) because the denominator contains prime factors other than 2 and 5.