What is 2/7 plus 7/18? (Answer: 85/126)

Exact Answer

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Problem: What is 2/7 plus 7/18?
Formula / Expression: 2/7 + 7/18
Final Answer: 85/126
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 18 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 18 = 126.
Working: LCD(7, 18) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 2/7 by 18, and multiply the numerator and denominator of 7/18 by 7 so both fractions share the common base 126.
Working: 2 × 18/7 × 18 = 36/126 and 7 × 7/18 × 7 = 49/126

Step 3: Add the Numerators
Now add the numerators (36 + 49 = 85) and keep the common denominator 126 unchanged.
Working: 36 + 49/126 = 85/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 126 is 1, confirming that 85/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 85/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 126 produces a repeating decimal (approximately 0.674603, or 67.4603%).
Working: 85 ÷ 126 = 0.674603 (67.4603%)

Key Values:
- Simplified Fraction: 85/126
- Mixed Number Form: 85/126
- Decimal Value: 0.674603
- Percentage: 67.4603%

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Solved with FractionsCalc:
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2/7 + 7/18 = 85/126

Simplified Fraction

85/126

Mixed Number

Proper (85/126)

Decimal Value

0.674603

Percentage

67.4603%

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Step-by-Step Solution: 2/7 + 7/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 18 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 18 = 126.

LCD(7, 18) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 2/7 by 18, and multiply the numerator and denominator of 7/18 by 7 so both fractions share the common base 126.

2 × 18/7 × 18 = 36/126 and 7 × 7/18 × 7 = 49/126

Step 3

Add the Numerators

Now add the numerators (36 + 49 = 85) and keep the common denominator 126 unchanged.

36 + 49/126 = 85/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 85 and 126 is 1, confirming that 85/126 cannot be reduced further—it is already in its simplest irreducible form.

85/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 126 produces a repeating decimal (approximately 0.674603, or 67.4603%).

85 ÷ 126 = 0.674603 (67.4603%)

Visual Representation

The diagram below illustrates 2/7 plus 7/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/126`
Mixed Number Form	`85/126`
Decimal Form	`0.674603`
Percentage	`67.4603%`

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Frequently Asked Questions

What is 2/7 plus 7/18 as a fraction?

2/7 + 7/18 in simplest fraction form is 85/126.

What is 2/7 plus 7/18 as a decimal?

2/7 + 7/18 converted to a decimal is 0.674603.

What is 2/7 plus 7/18 as a percentage?

2/7 + 7/18 expressed as a percentage is 67.4603%.

Does 2/7 plus 7/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.674603...) because the denominator contains prime factors other than 2 and 5.