What is 13/50 plus 7/13? (Answer: 519/650)

Exact Answer

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Problem: What is 13/50 plus 7/13?
Formula / Expression: 13/50 + 7/13
Final Answer: 519/650
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 50 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 13 = 650.
Working: LCD(50, 13) = 650

Step 2: Convert to Equivalent Fractions with Common Denominator 650
Multiply the numerator and denominator of 13/50 by 13, and multiply the numerator and denominator of 7/13 by 50 so both fractions share the common base 650.
Working: 13 × 13/50 × 13 = 169/650 and 7 × 50/13 × 50 = 350/650

Step 3: Add the Numerators
Now add the numerators (169 + 350 = 519) and keep the common denominator 650 unchanged.
Working: 169 + 350/650 = 519/650

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 519 and 650 is 1, confirming that 519/650 cannot be reduced further—it is already in its simplest irreducible form.
Working: 519/650

Step 5: Decimal & Percentage Representation
Dividing the numerator 519 by denominator 650 produces a repeating decimal (approximately 0.798462, or 79.8462%).
Working: 519 ÷ 650 = 0.798462 (79.8462%)

Key Values:
- Simplified Fraction: 519/650
- Mixed Number Form: 519/650
- Decimal Value: 0.798462
- Percentage: 79.8462%

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Solved with FractionsCalc:
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13/50 + 7/13 = 519/650

Simplified Fraction

519/650

Mixed Number

Proper (519/650)

Decimal Value

0.798462

Percentage

79.8462%

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Step-by-Step Solution: 13/50 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 50 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 13 = 650.

LCD(50, 13) = 650

Step 2

Convert to Equivalent Fractions with Common Denominator 650

Multiply the numerator and denominator of 13/50 by 13, and multiply the numerator and denominator of 7/13 by 50 so both fractions share the common base 650.

13 × 13/50 × 13 = 169/650 and 7 × 50/13 × 50 = 350/650

Step 3

Add the Numerators

Now add the numerators (169 + 350 = 519) and keep the common denominator 650 unchanged.

169 + 350/650 = 519/650

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 519 and 650 is 1, confirming that 519/650 cannot be reduced further—it is already in its simplest irreducible form.

519/650

Step 5

Decimal & Percentage Representation

Dividing the numerator 519 by denominator 650 produces a repeating decimal (approximately 0.798462, or 79.8462%).

519 ÷ 650 = 0.798462 (79.8462%)

Visual Representation

The diagram below illustrates 13/50 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`519/650`
Mixed Number Form	`519/650`
Decimal Form	`0.798462`
Percentage	`79.8462%`

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Frequently Asked Questions

What is 13/50 plus 7/13 as a fraction?

13/50 + 7/13 in simplest fraction form is 519/650.

What is 13/50 plus 7/13 as a decimal?

13/50 + 7/13 converted to a decimal is 0.798462.

What is 13/50 plus 7/13 as a percentage?

13/50 + 7/13 expressed as a percentage is 79.8462%.

Does 13/50 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.798462...) because the denominator contains prime factors other than 2 and 5.