What is 2/38 plus 2/3? (Answer: 41/57)

Exact Answer

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Problem: What is 2/38 plus 2/3?
Formula / Expression: 2/38 + 2/3
Final Answer: 41/57
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 3 = 114.
Working: LCD(38, 3) = 114

Step 2: Convert to Equivalent Fractions with Common Denominator 114
Multiply the numerator and denominator of 2/38 by 3, and multiply the numerator and denominator of 2/3 by 38 so both fractions share the common base 114.
Working: 2 × 3/38 × 3 = 6/114 and 2 × 38/3 × 38 = 76/114

Step 3: Add the Numerators
Now add the numerators (6 + 76 = 82) and keep the common denominator 114 unchanged.
Working: 6 + 76/114 = 82/114

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 114, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/114 ÷ 2 = 41/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 57 produces a repeating decimal (approximately 0.719298, or 71.9298%).
Working: 41 ÷ 57 = 0.719298 (71.9298%)

Key Values:
- Simplified Fraction: 41/57
- Mixed Number Form: 41/57
- Decimal Value: 0.719298
- Percentage: 71.9298%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-38-plus-2-3/
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2/38 + 2/3 = 41/57

Simplified Fraction

41/57

Mixed Number

Proper (41/57)

Decimal Value

0.719298

Percentage

71.9298%

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Step-by-Step Solution: 2/38 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 3 = 114.

LCD(38, 3) = 114

Step 2

Convert to Equivalent Fractions with Common Denominator 114

Multiply the numerator and denominator of 2/38 by 3, and multiply the numerator and denominator of 2/3 by 38 so both fractions share the common base 114.

2 × 3/38 × 3 = 6/114 and 2 × 38/3 × 38 = 76/114

Step 3

Add the Numerators

Now add the numerators (6 + 76 = 82) and keep the common denominator 114 unchanged.

6 + 76/114 = 82/114

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 114, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/114 ÷ 2 = 41/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 57 produces a repeating decimal (approximately 0.719298, or 71.9298%).

41 ÷ 57 = 0.719298 (71.9298%)

Visual Representation

The diagram below illustrates 2/38 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/57`
Mixed Number Form	`41/57`
Decimal Form	`0.719298`
Percentage	`71.9298%`

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Frequently Asked Questions

What is 2/38 plus 2/3 as a fraction?

2/38 + 2/3 in simplest fraction form is 41/57.

What is 2/38 plus 2/3 as a decimal?

2/38 + 2/3 converted to a decimal is 0.719298.

What is 2/38 plus 2/3 as a percentage?

2/38 + 2/3 expressed as a percentage is 71.9298%.

Does 2/38 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.719298...) because the denominator contains prime factors other than 2 and 5.