What is 2/38 plus 3/9? (Answer: 22/57)

Exact Answer

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Problem: What is 2/38 plus 3/9?
Formula / Expression: 2/38 + 3/9
Final Answer: 22/57
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 9 = 342.
Working: LCD(38, 9) = 342

Step 2: Convert to Equivalent Fractions with Common Denominator 342
Multiply the numerator and denominator of 2/38 by 9, and multiply the numerator and denominator of 3/9 by 38 so both fractions share the common base 342.
Working: 2 × 9/38 × 9 = 18/342 and 3 × 38/9 × 38 = 114/342

Step 3: Add the Numerators
Now add the numerators (18 + 114 = 132) and keep the common denominator 342 unchanged.
Working: 18 + 114/342 = 132/342

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 132 and 342, which is 6. Divide both the numerator and denominator by 6.
Working: 132 ÷ 6/342 ÷ 6 = 22/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 57 produces a repeating decimal (approximately 0.385965, or 38.5965%).
Working: 22 ÷ 57 = 0.385965 (38.5965%)

Key Values:
- Simplified Fraction: 22/57
- Mixed Number Form: 22/57
- Decimal Value: 0.385965
- Percentage: 38.5965%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-38-plus-3-9/
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2/38 + 3/9 = 22/57

Simplified Fraction

22/57

Mixed Number

Proper (22/57)

Decimal Value

0.385965

Percentage

38.5965%

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Step-by-Step Solution: 2/38 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 9 = 342.

LCD(38, 9) = 342

Step 2

Convert to Equivalent Fractions with Common Denominator 342

Multiply the numerator and denominator of 2/38 by 9, and multiply the numerator and denominator of 3/9 by 38 so both fractions share the common base 342.

2 × 9/38 × 9 = 18/342 and 3 × 38/9 × 38 = 114/342

Step 3

Add the Numerators

Now add the numerators (18 + 114 = 132) and keep the common denominator 342 unchanged.

18 + 114/342 = 132/342

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 132 and 342, which is 6. Divide both the numerator and denominator by 6.

132 ÷ 6/342 ÷ 6 = 22/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 57 produces a repeating decimal (approximately 0.385965, or 38.5965%).

22 ÷ 57 = 0.385965 (38.5965%)

Visual Representation

The diagram below illustrates 2/38 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/57`
Mixed Number Form	`22/57`
Decimal Form	`0.385965`
Percentage	`38.5965%`

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Frequently Asked Questions

What is 2/38 plus 3/9 as a fraction?

2/38 + 3/9 in simplest fraction form is 22/57.

What is 2/38 plus 3/9 as a decimal?

2/38 + 3/9 converted to a decimal is 0.385965.

What is 2/38 plus 3/9 as a percentage?

2/38 + 3/9 expressed as a percentage is 38.5965%.

Does 2/38 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.385965...) because the denominator contains prime factors other than 2 and 5.