What is 11/45 plus 5/13? (Answer: 368/585)

Exact Answer

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Problem: What is 11/45 plus 5/13?
Formula / Expression: 11/45 + 5/13
Final Answer: 368/585
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 45 × 13 = 585.
Working: LCD(45, 13) = 585

Step 2: Convert to Equivalent Fractions with Common Denominator 585
Multiply the numerator and denominator of 11/45 by 13, and multiply the numerator and denominator of 5/13 by 45 so both fractions share the common base 585.
Working: 11 × 13/45 × 13 = 143/585 and 5 × 45/13 × 45 = 225/585

Step 3: Add the Numerators
Now add the numerators (143 + 225 = 368) and keep the common denominator 585 unchanged.
Working: 143 + 225/585 = 368/585

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 368 and 585 is 1, confirming that 368/585 cannot be reduced further—it is already in its simplest irreducible form.
Working: 368/585

Step 5: Decimal & Percentage Representation
Dividing the numerator 368 by denominator 585 produces a repeating decimal (approximately 0.62906, or 62.906%).
Working: 368 ÷ 585 = 0.62906 (62.906%)

Key Values:
- Simplified Fraction: 368/585
- Mixed Number Form: 368/585
- Decimal Value: 0.62906
- Percentage: 62.906%

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Solved with FractionsCalc:
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11/45 + 5/13 = 368/585

Simplified Fraction

368/585

Mixed Number

Proper (368/585)

Decimal Value

0.62906

Percentage

62.906%

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Step-by-Step Solution: 11/45 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 45 × 13 = 585.

LCD(45, 13) = 585

Step 2

Convert to Equivalent Fractions with Common Denominator 585

Multiply the numerator and denominator of 11/45 by 13, and multiply the numerator and denominator of 5/13 by 45 so both fractions share the common base 585.

11 × 13/45 × 13 = 143/585 and 5 × 45/13 × 45 = 225/585

Step 3

Add the Numerators

Now add the numerators (143 + 225 = 368) and keep the common denominator 585 unchanged.

143 + 225/585 = 368/585

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 368 and 585 is 1, confirming that 368/585 cannot be reduced further—it is already in its simplest irreducible form.

368/585

Step 5

Decimal & Percentage Representation

Dividing the numerator 368 by denominator 585 produces a repeating decimal (approximately 0.62906, or 62.906%).

368 ÷ 585 = 0.62906 (62.906%)

Visual Representation

The diagram below illustrates 11/45 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`368/585`
Mixed Number Form	`368/585`
Decimal Form	`0.62906`
Percentage	`62.906%`

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Frequently Asked Questions

What is 11/45 plus 5/13 as a fraction?

11/45 + 5/13 in simplest fraction form is 368/585.

What is 11/45 plus 5/13 as a decimal?

11/45 + 5/13 converted to a decimal is 0.62906.

What is 11/45 plus 5/13 as a percentage?

11/45 + 5/13 expressed as a percentage is 62.906%.

Does 11/45 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.62906...) because the denominator contains prime factors other than 2 and 5.