What is 3/24 plus 11/13? (Answer: 101/104)

Exact Answer

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Problem: What is 3/24 plus 11/13?
Formula / Expression: 3/24 + 11/13
Final Answer: 101/104
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 24 × 13 = 312.
Working: LCD(24, 13) = 312

Step 2: Convert to Equivalent Fractions with Common Denominator 312
Multiply the numerator and denominator of 3/24 by 13, and multiply the numerator and denominator of 11/13 by 24 so both fractions share the common base 312.
Working: 3 × 13/24 × 13 = 39/312 and 11 × 24/13 × 24 = 264/312

Step 3: Add the Numerators
Now add the numerators (39 + 264 = 303) and keep the common denominator 312 unchanged.
Working: 39 + 264/312 = 303/312

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 303 and 312, which is 3. Divide both the numerator and denominator by 3.
Working: 303 ÷ 3/312 ÷ 3 = 101/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 104 produces a repeating decimal (approximately 0.971154, or 97.1154%).
Working: 101 ÷ 104 = 0.971154 (97.1154%)

Key Values:
- Simplified Fraction: 101/104
- Mixed Number Form: 101/104
- Decimal Value: 0.971154
- Percentage: 97.1154%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-24-plus-11-13/
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3/24 + 11/13 = 101/104

Simplified Fraction

101/104

Mixed Number

Proper (101/104)

Decimal Value

0.971154

Percentage

97.1154%

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Step-by-Step Solution: 3/24 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 24 × 13 = 312.

LCD(24, 13) = 312

Step 2

Convert to Equivalent Fractions with Common Denominator 312

Multiply the numerator and denominator of 3/24 by 13, and multiply the numerator and denominator of 11/13 by 24 so both fractions share the common base 312.

3 × 13/24 × 13 = 39/312 and 11 × 24/13 × 24 = 264/312

Step 3

Add the Numerators

Now add the numerators (39 + 264 = 303) and keep the common denominator 312 unchanged.

39 + 264/312 = 303/312

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 303 and 312, which is 3. Divide both the numerator and denominator by 3.

303 ÷ 3/312 ÷ 3 = 101/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 104 produces a repeating decimal (approximately 0.971154, or 97.1154%).

101 ÷ 104 = 0.971154 (97.1154%)

Visual Representation

The diagram below illustrates 3/24 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/104`
Mixed Number Form	`101/104`
Decimal Form	`0.971154`
Percentage	`97.1154%`

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Frequently Asked Questions

What is 3/24 plus 11/13 as a fraction?

3/24 + 11/13 in simplest fraction form is 101/104.

What is 3/24 plus 11/13 as a decimal?

3/24 + 11/13 converted to a decimal is 0.971154.

What is 3/24 plus 11/13 as a percentage?

3/24 + 11/13 expressed as a percentage is 97.1154%.

Does 3/24 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.971154...) because the denominator contains prime factors other than 2 and 5.