What is 11/40 plus 5/13? (Answer: 343/520)

Exact Answer

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Problem: What is 11/40 plus 5/13?
Formula / Expression: 11/40 + 5/13
Final Answer: 343/520
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.
Working: LCD(40, 13) = 520

Step 2: Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 11/40 by 13, and multiply the numerator and denominator of 5/13 by 40 so both fractions share the common base 520.
Working: 11 × 13/40 × 13 = 143/520 and 5 × 40/13 × 40 = 200/520

Step 3: Add the Numerators
Now add the numerators (143 + 200 = 343) and keep the common denominator 520 unchanged.
Working: 143 + 200/520 = 343/520

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 343 and 520 is 1, confirming that 343/520 cannot be reduced further—it is already in its simplest irreducible form.
Working: 343/520

Step 5: Decimal & Percentage Representation
Dividing the numerator 343 by denominator 520 produces a repeating decimal (approximately 0.659615, or 65.9615%).
Working: 343 ÷ 520 = 0.659615 (65.9615%)

Key Values:
- Simplified Fraction: 343/520
- Mixed Number Form: 343/520
- Decimal Value: 0.659615
- Percentage: 65.9615%

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11/40 + 5/13 = 343/520

Simplified Fraction

343/520

Mixed Number

Proper (343/520)

Decimal Value

0.659615

Percentage

65.9615%

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Step-by-Step Solution: 11/40 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.

LCD(40, 13) = 520

Step 2

Convert to Equivalent Fractions with Common Denominator 520

Multiply the numerator and denominator of 11/40 by 13, and multiply the numerator and denominator of 5/13 by 40 so both fractions share the common base 520.

11 × 13/40 × 13 = 143/520 and 5 × 40/13 × 40 = 200/520

Step 3

Add the Numerators

Now add the numerators (143 + 200 = 343) and keep the common denominator 520 unchanged.

143 + 200/520 = 343/520

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 343 and 520 is 1, confirming that 343/520 cannot be reduced further—it is already in its simplest irreducible form.

343/520

Step 5

Decimal & Percentage Representation

Dividing the numerator 343 by denominator 520 produces a repeating decimal (approximately 0.659615, or 65.9615%).

343 ÷ 520 = 0.659615 (65.9615%)

Visual Representation

The diagram below illustrates 11/40 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`343/520`
Mixed Number Form	`343/520`
Decimal Form	`0.659615`
Percentage	`65.9615%`

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Frequently Asked Questions

What is 11/40 plus 5/13 as a fraction?

11/40 + 5/13 in simplest fraction form is 343/520.

What is 11/40 plus 5/13 as a decimal?

11/40 + 5/13 converted to a decimal is 0.659615.

What is 11/40 plus 5/13 as a percentage?

11/40 + 5/13 expressed as a percentage is 65.9615%.

Does 11/40 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.659615...) because the denominator contains prime factors other than 2 and 5.