What is 2/38 plus 2/7? (Answer: 45/133)

Exact Answer

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Problem: What is 2/38 plus 2/7?
Formula / Expression: 2/38 + 2/7
Final Answer: 45/133
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 7 = 266.
Working: LCD(38, 7) = 266

Step 2: Convert to Equivalent Fractions with Common Denominator 266
Multiply the numerator and denominator of 2/38 by 7, and multiply the numerator and denominator of 2/7 by 38 so both fractions share the common base 266.
Working: 2 × 7/38 × 7 = 14/266 and 2 × 38/7 × 38 = 76/266

Step 3: Add the Numerators
Now add the numerators (14 + 76 = 90) and keep the common denominator 266 unchanged.
Working: 14 + 76/266 = 90/266

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 266, which is 2. Divide both the numerator and denominator by 2.
Working: 90 ÷ 2/266 ÷ 2 = 45/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 133 produces a repeating decimal (approximately 0.338346, or 33.8346%).
Working: 45 ÷ 133 = 0.338346 (33.8346%)

Key Values:
- Simplified Fraction: 45/133
- Mixed Number Form: 45/133
- Decimal Value: 0.338346
- Percentage: 33.8346%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-38-plus-2-7/
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2/38 + 2/7 = 45/133

Simplified Fraction

45/133

Mixed Number

Proper (45/133)

Decimal Value

0.338346

Percentage

33.8346%

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Step-by-Step Solution: 2/38 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 7 = 266.

LCD(38, 7) = 266

Step 2

Convert to Equivalent Fractions with Common Denominator 266

Multiply the numerator and denominator of 2/38 by 7, and multiply the numerator and denominator of 2/7 by 38 so both fractions share the common base 266.

2 × 7/38 × 7 = 14/266 and 2 × 38/7 × 38 = 76/266

Step 3

Add the Numerators

Now add the numerators (14 + 76 = 90) and keep the common denominator 266 unchanged.

14 + 76/266 = 90/266

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 266, which is 2. Divide both the numerator and denominator by 2.

90 ÷ 2/266 ÷ 2 = 45/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 133 produces a repeating decimal (approximately 0.338346, or 33.8346%).

45 ÷ 133 = 0.338346 (33.8346%)

Visual Representation

The diagram below illustrates 2/38 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/133`
Mixed Number Form	`45/133`
Decimal Form	`0.338346`
Percentage	`33.8346%`

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Frequently Asked Questions

What is 2/38 plus 2/7 as a fraction?

2/38 + 2/7 in simplest fraction form is 45/133.

What is 2/38 plus 2/7 as a decimal?

2/38 + 2/7 converted to a decimal is 0.338346.

What is 2/38 plus 2/7 as a percentage?

2/38 + 2/7 expressed as a percentage is 33.8346%.

Does 2/38 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.338346...) because the denominator contains prime factors other than 2 and 5.