What is 7/18 plus 3/7? (Answer: 103/126)

Exact Answer

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Problem: What is 7/18 plus 3/7?
Formula / Expression: 7/18 + 3/7
Final Answer: 103/126
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 7/18 by 7, and multiply the numerator and denominator of 3/7 by 18 so both fractions share the common base 126.
Working: 7 × 7/18 × 7 = 49/126 and 3 × 18/7 × 18 = 54/126

Step 3: Add the Numerators
Now add the numerators (49 + 54 = 103) and keep the common denominator 126 unchanged.
Working: 49 + 54/126 = 103/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 126 is 1, confirming that 103/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 126 produces a repeating decimal (approximately 0.81746, or 81.746%).
Working: 103 ÷ 126 = 0.81746 (81.746%)

Key Values:
- Simplified Fraction: 103/126
- Mixed Number Form: 103/126
- Decimal Value: 0.81746
- Percentage: 81.746%

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7/18 + 3/7 = 103/126

Simplified Fraction

103/126

Mixed Number

Proper (103/126)

Decimal Value

0.81746

Percentage

81.746%

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Step-by-Step Solution: 7/18 + 3/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(18, 7) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 7/18 by 7, and multiply the numerator and denominator of 3/7 by 18 so both fractions share the common base 126.

7 × 7/18 × 7 = 49/126 and 3 × 18/7 × 18 = 54/126

Step 3

Add the Numerators

Now add the numerators (49 + 54 = 103) and keep the common denominator 126 unchanged.

49 + 54/126 = 103/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 126 is 1, confirming that 103/126 cannot be reduced further—it is already in its simplest irreducible form.

103/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 126 produces a repeating decimal (approximately 0.81746, or 81.746%).

103 ÷ 126 = 0.81746 (81.746%)

Visual Representation

The diagram below illustrates 7/18 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/126`
Mixed Number Form	`103/126`
Decimal Form	`0.81746`
Percentage	`81.746%`

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Frequently Asked Questions

What is 7/18 plus 3/7 as a fraction?

7/18 + 3/7 in simplest fraction form is 103/126.

What is 7/18 plus 3/7 as a decimal?

7/18 + 3/7 converted to a decimal is 0.81746.

What is 7/18 plus 3/7 as a percentage?

7/18 + 3/7 expressed as a percentage is 81.746%.

Does 7/18 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.81746...) because the denominator contains prime factors other than 2 and 5.