What is 2/23 plus 3/4? (Answer: 77/92)

Exact Answer

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Problem: What is 2/23 plus 3/4?
Formula / Expression: 2/23 + 3/4
Final Answer: 77/92
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 4 = 92.
Working: LCD(23, 4) = 92

Step 2: Convert to Equivalent Fractions with Common Denominator 92
Multiply the numerator and denominator of 2/23 by 4, and multiply the numerator and denominator of 3/4 by 23 so both fractions share the common base 92.
Working: 2 × 4/23 × 4 = 8/92 and 3 × 23/4 × 23 = 69/92

Step 3: Add the Numerators
Now add the numerators (8 + 69 = 77) and keep the common denominator 92 unchanged.
Working: 8 + 69/92 = 77/92

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 92 is 1, confirming that 77/92 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/92

Step 5: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 92 produces a repeating decimal (approximately 0.836957, or 83.6957%).
Working: 77 ÷ 92 = 0.836957 (83.6957%)

Key Values:
- Simplified Fraction: 77/92
- Mixed Number Form: 77/92
- Decimal Value: 0.836957
- Percentage: 83.6957%

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Solved with FractionsCalc:
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2/23 + 3/4 = 77/92

Simplified Fraction

77/92

Mixed Number

Proper (77/92)

Decimal Value

0.836957

Percentage

83.6957%

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Step-by-Step Solution: 2/23 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 4 = 92.

LCD(23, 4) = 92

Step 2

Convert to Equivalent Fractions with Common Denominator 92

Multiply the numerator and denominator of 2/23 by 4, and multiply the numerator and denominator of 3/4 by 23 so both fractions share the common base 92.

2 × 4/23 × 4 = 8/92 and 3 × 23/4 × 23 = 69/92

Step 3

Add the Numerators

Now add the numerators (8 + 69 = 77) and keep the common denominator 92 unchanged.

8 + 69/92 = 77/92

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 92 is 1, confirming that 77/92 cannot be reduced further—it is already in its simplest irreducible form.

77/92

Step 5

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 92 produces a repeating decimal (approximately 0.836957, or 83.6957%).

77 ÷ 92 = 0.836957 (83.6957%)

Visual Representation

The diagram below illustrates 2/23 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/92`
Mixed Number Form	`77/92`
Decimal Form	`0.836957`
Percentage	`83.6957%`

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Frequently Asked Questions

What is 2/23 plus 3/4 as a fraction?

2/23 + 3/4 in simplest fraction form is 77/92.

What is 2/23 plus 3/4 as a decimal?

2/23 + 3/4 converted to a decimal is 0.836957.

What is 2/23 plus 3/4 as a percentage?

2/23 + 3/4 expressed as a percentage is 83.6957%.

Does 2/23 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.836957...) because the denominator contains prime factors other than 2 and 5.