What is 2/7 plus 10/18? (Answer: 53/63)

Exact Answer

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Problem: What is 2/7 plus 10/18?
Formula / Expression: 2/7 + 10/18
Final Answer: 53/63
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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 10/18 by 7 so both fractions share the common base 126.
Working: 2 × 18/7 × 18 = 36/126 and 10 × 7/18 × 7 = 70/126

Step 3: Add the Numerators
Now add the numerators (36 + 70 = 106) and keep the common denominator 126 unchanged.
Working: 36 + 70/126 = 106/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 106 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 106 ÷ 2/126 ÷ 2 = 53/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 63 produces a repeating decimal (approximately 0.84127, or 84.127%).
Working: 53 ÷ 63 = 0.84127 (84.127%)

Key Values:
- Simplified Fraction: 53/63
- Mixed Number Form: 53/63
- Decimal Value: 0.84127
- Percentage: 84.127%

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Solved with FractionsCalc:
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2/7 + 10/18 = 53/63

Simplified Fraction

53/63

Mixed Number

Proper (53/63)

Decimal Value

0.84127

Percentage

84.127%

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Step-by-Step Solution: 2/7 + 10/18

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 10/18 by 7 so both fractions share the common base 126.

2 × 18/7 × 18 = 36/126 and 10 × 7/18 × 7 = 70/126

Step 3

Add the Numerators

Now add the numerators (36 + 70 = 106) and keep the common denominator 126 unchanged.

36 + 70/126 = 106/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 106 and 126, which is 2. Divide both the numerator and denominator by 2.

106 ÷ 2/126 ÷ 2 = 53/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 63 produces a repeating decimal (approximately 0.84127, or 84.127%).

53 ÷ 63 = 0.84127 (84.127%)

Visual Representation

The diagram below illustrates 2/7 plus 10/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/63`
Mixed Number Form	`53/63`
Decimal Form	`0.84127`
Percentage	`84.127%`

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Frequently Asked Questions

What is 2/7 plus 10/18 as a fraction?

2/7 + 10/18 in simplest fraction form is 53/63.

What is 2/7 plus 10/18 as a decimal?

2/7 + 10/18 converted to a decimal is 0.84127.

What is 2/7 plus 10/18 as a percentage?

2/7 + 10/18 expressed as a percentage is 84.127%.

Does 2/7 plus 10/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.84127...) because the denominator contains prime factors other than 2 and 5.