What is 3/38 plus 2/3? (Answer: 85/114)

Exact Answer

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Problem: What is 3/38 plus 2/3?
Formula / Expression: 3/38 + 2/3
Final Answer: 85/114
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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 3/38 by 3, and multiply the numerator and denominator of 2/3 by 38 so both fractions share the common base 114.
Working: 3 × 3/38 × 3 = 9/114 and 2 × 38/3 × 38 = 76/114

Step 3: Add the Numerators
Now add the numerators (9 + 76 = 85) and keep the common denominator 114 unchanged.
Working: 9 + 76/114 = 85/114

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 114 is 1, confirming that 85/114 cannot be reduced further—it is already in its simplest irreducible form.
Working: 85/114

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 114 produces a repeating decimal (approximately 0.745614, or 74.5614%).
Working: 85 ÷ 114 = 0.745614 (74.5614%)

Key Values:
- Simplified Fraction: 85/114
- Mixed Number Form: 85/114
- Decimal Value: 0.745614
- Percentage: 74.5614%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-38-plus-2-3/
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3/38 + 2/3 = 85/114

Simplified Fraction

85/114

Mixed Number

Proper (85/114)

Decimal Value

0.745614

Percentage

74.5614%

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Step-by-Step Solution: 3/38 + 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 3/38 by 3, and multiply the numerator and denominator of 2/3 by 38 so both fractions share the common base 114.

3 × 3/38 × 3 = 9/114 and 2 × 38/3 × 38 = 76/114

Step 3

Add the Numerators

Now add the numerators (9 + 76 = 85) and keep the common denominator 114 unchanged.

9 + 76/114 = 85/114

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 85 and 114 is 1, confirming that 85/114 cannot be reduced further—it is already in its simplest irreducible form.

85/114

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 114 produces a repeating decimal (approximately 0.745614, or 74.5614%).

85 ÷ 114 = 0.745614 (74.5614%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/114`
Mixed Number Form	`85/114`
Decimal Form	`0.745614`
Percentage	`74.5614%`

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Frequently Asked Questions

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

3/38 + 2/3 in simplest fraction form is 85/114.

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

3/38 + 2/3 converted to a decimal is 0.745614.

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

3/38 + 2/3 expressed as a percentage is 74.5614%.

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

It results in a repeating decimal (approximately 0.745614...) because the denominator contains prime factors other than 2 and 5.