What is 3/24 plus 10/13? (Answer: 93/104)

Exact Answer

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Problem: What is 3/24 plus 10/13?
Formula / Expression: 3/24 + 10/13
Final Answer: 93/104
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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 10/13 by 24 so both fractions share the common base 312.
Working: 3 × 13/24 × 13 = 39/312 and 10 × 24/13 × 24 = 240/312

Step 3: Add the Numerators
Now add the numerators (39 + 240 = 279) and keep the common denominator 312 unchanged.
Working: 39 + 240/312 = 279/312

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 279 and 312, which is 3. Divide both the numerator and denominator by 3.
Working: 279 ÷ 3/312 ÷ 3 = 93/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 93 by denominator 104 produces a repeating decimal (approximately 0.894231, or 89.4231%).
Working: 93 ÷ 104 = 0.894231 (89.4231%)

Key Values:
- Simplified Fraction: 93/104
- Mixed Number Form: 93/104
- Decimal Value: 0.894231
- Percentage: 89.4231%

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Solved with FractionsCalc:
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3/24 + 10/13 = 93/104

Simplified Fraction

93/104

Mixed Number

Proper (93/104)

Decimal Value

0.894231

Percentage

89.4231%

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Step-by-Step Solution: 3/24 + 10/13

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 10/13 by 24 so both fractions share the common base 312.

3 × 13/24 × 13 = 39/312 and 10 × 24/13 × 24 = 240/312

Step 3

Add the Numerators

Now add the numerators (39 + 240 = 279) and keep the common denominator 312 unchanged.

39 + 240/312 = 279/312

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 279 and 312, which is 3. Divide both the numerator and denominator by 3.

279 ÷ 3/312 ÷ 3 = 93/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 93 by denominator 104 produces a repeating decimal (approximately 0.894231, or 89.4231%).

93 ÷ 104 = 0.894231 (89.4231%)

Visual Representation

The diagram below illustrates 3/24 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`93/104`
Mixed Number Form	`93/104`
Decimal Form	`0.894231`
Percentage	`89.4231%`

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Frequently Asked Questions

What is 3/24 plus 10/13 as a fraction?

3/24 + 10/13 in simplest fraction form is 93/104.

What is 3/24 plus 10/13 as a decimal?

3/24 + 10/13 converted to a decimal is 0.894231.

What is 3/24 plus 10/13 as a percentage?

3/24 + 10/13 expressed as a percentage is 89.4231%.

Does 3/24 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.894231...) because the denominator contains prime factors other than 2 and 5.