What is 11/23 plus 2/4? (Answer: 45/46)

Exact Answer

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Problem: What is 11/23 plus 2/4?
Formula / Expression: 11/23 + 2/4
Final Answer: 45/46
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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 11/23 by 4, and multiply the numerator and denominator of 2/4 by 23 so both fractions share the common base 92.
Working: 11 × 4/23 × 4 = 44/92 and 2 × 23/4 × 23 = 46/92

Step 3: Add the Numerators
Now add the numerators (44 + 46 = 90) and keep the common denominator 92 unchanged.
Working: 44 + 46/92 = 90/92

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 92, which is 2. Divide both the numerator and denominator by 2.
Working: 90 ÷ 2/92 ÷ 2 = 45/46

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 46 produces a repeating decimal (approximately 0.978261, or 97.8261%).
Working: 45 ÷ 46 = 0.978261 (97.8261%)

Key Values:
- Simplified Fraction: 45/46
- Mixed Number Form: 45/46
- Decimal Value: 0.978261
- Percentage: 97.8261%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-23-plus-2-4/
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11/23 + 2/4 = 45/46

Simplified Fraction

45/46

Mixed Number

Proper (45/46)

Decimal Value

0.978261

Percentage

97.8261%

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Step-by-Step Solution: 11/23 + 2/4

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 11/23 by 4, and multiply the numerator and denominator of 2/4 by 23 so both fractions share the common base 92.

11 × 4/23 × 4 = 44/92 and 2 × 23/4 × 23 = 46/92

Step 3

Add the Numerators

Now add the numerators (44 + 46 = 90) and keep the common denominator 92 unchanged.

44 + 46/92 = 90/92

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 92, which is 2. Divide both the numerator and denominator by 2.

90 ÷ 2/92 ÷ 2 = 45/46

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 46 produces a repeating decimal (approximately 0.978261, or 97.8261%).

45 ÷ 46 = 0.978261 (97.8261%)

Visual Representation

The diagram below illustrates 11/23 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/46`
Mixed Number Form	`45/46`
Decimal Form	`0.978261`
Percentage	`97.8261%`

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Frequently Asked Questions

What is 11/23 plus 2/4 as a fraction?

11/23 + 2/4 in simplest fraction form is 45/46.

What is 11/23 plus 2/4 as a decimal?

11/23 + 2/4 converted to a decimal is 0.978261.

What is 11/23 plus 2/4 as a percentage?

11/23 + 2/4 expressed as a percentage is 97.8261%.

Does 11/23 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.978261...) because the denominator contains prime factors other than 2 and 5.