What is 2/18 plus 5/7? (Answer: 52/63)

Exact Answer

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Problem: What is 2/18 plus 5/7?
Formula / Expression: 2/18 + 5/7
Final Answer: 52/63
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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 2/18 by 7, and multiply the numerator and denominator of 5/7 by 18 so both fractions share the common base 126.
Working: 2 × 7/18 × 7 = 14/126 and 5 × 18/7 × 18 = 90/126

Step 3: Add the Numerators
Now add the numerators (14 + 90 = 104) and keep the common denominator 126 unchanged.
Working: 14 + 90/126 = 104/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 104 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 104 ÷ 2/126 ÷ 2 = 52/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 63 produces a repeating decimal (approximately 0.825397, or 82.5397%).
Working: 52 ÷ 63 = 0.825397 (82.5397%)

Key Values:
- Simplified Fraction: 52/63
- Mixed Number Form: 52/63
- Decimal Value: 0.825397
- Percentage: 82.5397%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-18-plus-5-7/
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2/18 + 5/7 = 52/63

Simplified Fraction

52/63

Mixed Number

Proper (52/63)

Decimal Value

0.825397

Percentage

82.5397%

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Step-by-Step Solution: 2/18 + 5/7

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 2/18 by 7, and multiply the numerator and denominator of 5/7 by 18 so both fractions share the common base 126.

2 × 7/18 × 7 = 14/126 and 5 × 18/7 × 18 = 90/126

Step 3

Add the Numerators

Now add the numerators (14 + 90 = 104) and keep the common denominator 126 unchanged.

14 + 90/126 = 104/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 104 and 126, which is 2. Divide both the numerator and denominator by 2.

104 ÷ 2/126 ÷ 2 = 52/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 63 produces a repeating decimal (approximately 0.825397, or 82.5397%).

52 ÷ 63 = 0.825397 (82.5397%)

Visual Representation

The diagram below illustrates 2/18 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/63`
Mixed Number Form	`52/63`
Decimal Form	`0.825397`
Percentage	`82.5397%`

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Frequently Asked Questions

What is 2/18 plus 5/7 as a fraction?

2/18 + 5/7 in simplest fraction form is 52/63.

What is 2/18 plus 5/7 as a decimal?

2/18 + 5/7 converted to a decimal is 0.825397.

What is 2/18 plus 5/7 as a percentage?

2/18 + 5/7 expressed as a percentage is 82.5397%.

Does 2/18 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.825397...) because the denominator contains prime factors other than 2 and 5.