What is 7/24 plus 5/13? (Answer: 211/312)

Exact Answer

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Problem: What is 7/24 plus 5/13?
Formula / Expression: 7/24 + 5/13
Final Answer: 211/312
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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 7/24 by 13, and multiply the numerator and denominator of 5/13 by 24 so both fractions share the common base 312.
Working: 7 × 13/24 × 13 = 91/312 and 5 × 24/13 × 24 = 120/312

Step 3: Add the Numerators
Now add the numerators (91 + 120 = 211) and keep the common denominator 312 unchanged.
Working: 91 + 120/312 = 211/312

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 211 and 312 is 1, confirming that 211/312 cannot be reduced further—it is already in its simplest irreducible form.
Working: 211/312

Step 5: Decimal & Percentage Representation
Dividing the numerator 211 by denominator 312 produces a repeating decimal (approximately 0.676282, or 67.6282%).
Working: 211 ÷ 312 = 0.676282 (67.6282%)

Key Values:
- Simplified Fraction: 211/312
- Mixed Number Form: 211/312
- Decimal Value: 0.676282
- Percentage: 67.6282%

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Solved with FractionsCalc:
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7/24 + 5/13 = 211/312

Simplified Fraction

211/312

Mixed Number

Proper (211/312)

Decimal Value

0.676282

Percentage

67.6282%

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Step-by-Step Solution: 7/24 + 5/13

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 7/24 by 13, and multiply the numerator and denominator of 5/13 by 24 so both fractions share the common base 312.

7 × 13/24 × 13 = 91/312 and 5 × 24/13 × 24 = 120/312

Step 3

Add the Numerators

Now add the numerators (91 + 120 = 211) and keep the common denominator 312 unchanged.

91 + 120/312 = 211/312

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 211 and 312 is 1, confirming that 211/312 cannot be reduced further—it is already in its simplest irreducible form.

211/312

Step 5

Decimal & Percentage Representation

Dividing the numerator 211 by denominator 312 produces a repeating decimal (approximately 0.676282, or 67.6282%).

211 ÷ 312 = 0.676282 (67.6282%)

Visual Representation

The diagram below illustrates 7/24 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`211/312`
Mixed Number Form	`211/312`
Decimal Form	`0.676282`
Percentage	`67.6282%`

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Frequently Asked Questions

What is 7/24 plus 5/13 as a fraction?

7/24 + 5/13 in simplest fraction form is 211/312.

What is 7/24 plus 5/13 as a decimal?

7/24 + 5/13 converted to a decimal is 0.676282.

What is 7/24 plus 5/13 as a percentage?

7/24 + 5/13 expressed as a percentage is 67.6282%.

Does 7/24 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.676282...) because the denominator contains prime factors other than 2 and 5.