What is 2/36 plus 3/7? (Answer: 61/126)

Exact Answer

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Problem: What is 2/36 plus 3/7?
Formula / Expression: 2/36 + 3/7
Final Answer: 61/126
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 7 = 252.
Working: LCD(36, 7) = 252

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 2/36 by 7, and multiply the numerator and denominator of 3/7 by 36 so both fractions share the common base 252.
Working: 2 × 7/36 × 7 = 14/252 and 3 × 36/7 × 36 = 108/252

Step 3: Add the Numerators
Now add the numerators (14 + 108 = 122) and keep the common denominator 252 unchanged.
Working: 14 + 108/252 = 122/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 122 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: 122 ÷ 2/252 ÷ 2 = 61/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 126 produces a repeating decimal (approximately 0.484127, or 48.4127%).
Working: 61 ÷ 126 = 0.484127 (48.4127%)

Key Values:
- Simplified Fraction: 61/126
- Mixed Number Form: 61/126
- Decimal Value: 0.484127
- Percentage: 48.4127%

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Solved with FractionsCalc:
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2/36 + 3/7 = 61/126

Simplified Fraction

61/126

Mixed Number

Proper (61/126)

Decimal Value

0.484127

Percentage

48.4127%

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Step-by-Step Solution: 2/36 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 7 = 252.

LCD(36, 7) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 2/36 by 7, and multiply the numerator and denominator of 3/7 by 36 so both fractions share the common base 252.

2 × 7/36 × 7 = 14/252 and 3 × 36/7 × 36 = 108/252

Step 3

Add the Numerators

Now add the numerators (14 + 108 = 122) and keep the common denominator 252 unchanged.

14 + 108/252 = 122/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 122 and 252, which is 2. Divide both the numerator and denominator by 2.

122 ÷ 2/252 ÷ 2 = 61/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 126 produces a repeating decimal (approximately 0.484127, or 48.4127%).

61 ÷ 126 = 0.484127 (48.4127%)

Visual Representation

The diagram below illustrates 2/36 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/126`
Mixed Number Form	`61/126`
Decimal Form	`0.484127`
Percentage	`48.4127%`

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Frequently Asked Questions

What is 2/36 plus 3/7 as a fraction?

2/36 + 3/7 in simplest fraction form is 61/126.

What is 2/36 plus 3/7 as a decimal?

2/36 + 3/7 converted to a decimal is 0.484127.

What is 2/36 plus 3/7 as a percentage?

2/36 + 3/7 expressed as a percentage is 48.4127%.

Does 2/36 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.484127...) because the denominator contains prime factors other than 2 and 5.