What is 2/38 plus 3/4? (Answer: 61/76)

Exact Answer

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Problem: What is 2/38 plus 3/4?
Formula / Expression: 2/38 + 3/4
Final Answer: 61/76
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 76 (which is smaller than their product 38 × 4 = 152, keeping the calculation simpler).
Working: LCD(38, 4) = 76

Step 2: Convert to Equivalent Fractions with Common Denominator 76
Multiply the numerator and denominator of 2/38 by 2, and multiply the numerator and denominator of 3/4 by 19 so both fractions share the common base 76.
Working: 2 × 2/38 × 2 = 4/76 and 3 × 19/4 × 19 = 57/76

Step 3: Add the Numerators
Now add the numerators (4 + 57 = 61) and keep the common denominator 76 unchanged.
Working: 4 + 57/76 = 61/76

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 76 is 1, confirming that 61/76 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/76

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 76 produces a repeating decimal (approximately 0.802632, or 80.2632%).
Working: 61 ÷ 76 = 0.802632 (80.2632%)

Key Values:
- Simplified Fraction: 61/76
- Mixed Number Form: 61/76
- Decimal Value: 0.802632
- Percentage: 80.2632%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-38-plus-3-4/
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2/38 + 3/4 = 61/76

Simplified Fraction

61/76

Mixed Number

Proper (61/76)

Decimal Value

0.802632

Percentage

80.2632%

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Step-by-Step Solution: 2/38 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 76 (which is smaller than their product 38 × 4 = 152, keeping the calculation simpler).

LCD(38, 4) = 76

Step 2

Convert to Equivalent Fractions with Common Denominator 76

Multiply the numerator and denominator of 2/38 by 2, and multiply the numerator and denominator of 3/4 by 19 so both fractions share the common base 76.

2 × 2/38 × 2 = 4/76 and 3 × 19/4 × 19 = 57/76

Step 3

Add the Numerators

Now add the numerators (4 + 57 = 61) and keep the common denominator 76 unchanged.

4 + 57/76 = 61/76

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 76 is 1, confirming that 61/76 cannot be reduced further—it is already in its simplest irreducible form.

61/76

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 76 produces a repeating decimal (approximately 0.802632, or 80.2632%).

61 ÷ 76 = 0.802632 (80.2632%)

Visual Representation

The diagram below illustrates 2/38 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/76`
Mixed Number Form	`61/76`
Decimal Form	`0.802632`
Percentage	`80.2632%`

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Frequently Asked Questions

What is 2/38 plus 3/4 as a fraction?

2/38 + 3/4 in simplest fraction form is 61/76.

What is 2/38 plus 3/4 as a decimal?

2/38 + 3/4 converted to a decimal is 0.802632.

What is 2/38 plus 3/4 as a percentage?

2/38 + 3/4 expressed as a percentage is 80.2632%.

Does 2/38 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.802632...) because the denominator contains prime factors other than 2 and 5.