What is 3/44 plus 5/13? (Answer: 259/572)

Exact Answer

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Problem: What is 3/44 plus 5/13?
Formula / Expression: 3/44 + 5/13
Final Answer: 259/572
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 44 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 44 × 13 = 572.
Working: LCD(44, 13) = 572

Step 2: Convert to Equivalent Fractions with Common Denominator 572
Multiply the numerator and denominator of 3/44 by 13, and multiply the numerator and denominator of 5/13 by 44 so both fractions share the common base 572.
Working: 3 × 13/44 × 13 = 39/572 and 5 × 44/13 × 44 = 220/572

Step 3: Add the Numerators
Now add the numerators (39 + 220 = 259) and keep the common denominator 572 unchanged.
Working: 39 + 220/572 = 259/572

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 259 and 572 is 1, confirming that 259/572 cannot be reduced further—it is already in its simplest irreducible form.
Working: 259/572

Step 5: Decimal & Percentage Representation
Dividing the numerator 259 by denominator 572 produces a repeating decimal (approximately 0.452797, or 45.2797%).
Working: 259 ÷ 572 = 0.452797 (45.2797%)

Key Values:
- Simplified Fraction: 259/572
- Mixed Number Form: 259/572
- Decimal Value: 0.452797
- Percentage: 45.2797%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-44-plus-5-13/
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3/44 + 5/13 = 259/572

Simplified Fraction

259/572

Mixed Number

Proper (259/572)

Decimal Value

0.452797

Percentage

45.2797%

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Step-by-Step Solution: 3/44 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 44 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 44 × 13 = 572.

LCD(44, 13) = 572

Step 2

Convert to Equivalent Fractions with Common Denominator 572

Multiply the numerator and denominator of 3/44 by 13, and multiply the numerator and denominator of 5/13 by 44 so both fractions share the common base 572.

3 × 13/44 × 13 = 39/572 and 5 × 44/13 × 44 = 220/572

Step 3

Add the Numerators

Now add the numerators (39 + 220 = 259) and keep the common denominator 572 unchanged.

39 + 220/572 = 259/572

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 259 and 572 is 1, confirming that 259/572 cannot be reduced further—it is already in its simplest irreducible form.

259/572

Step 5

Decimal & Percentage Representation

Dividing the numerator 259 by denominator 572 produces a repeating decimal (approximately 0.452797, or 45.2797%).

259 ÷ 572 = 0.452797 (45.2797%)

Visual Representation

The diagram below illustrates 3/44 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`259/572`
Mixed Number Form	`259/572`
Decimal Form	`0.452797`
Percentage	`45.2797%`

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Frequently Asked Questions

What is 3/44 plus 5/13 as a fraction?

3/44 + 5/13 in simplest fraction form is 259/572.

What is 3/44 plus 5/13 as a decimal?

3/44 + 5/13 converted to a decimal is 0.452797.

What is 3/44 plus 5/13 as a percentage?

3/44 + 5/13 expressed as a percentage is 45.2797%.

Does 3/44 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452797...) because the denominator contains prime factors other than 2 and 5.