What is 3/43 plus 4/13? (Answer: 211/559)

Exact Answer

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Problem: What is 3/43 plus 4/13?
Formula / Expression: 3/43 + 4/13
Final Answer: 211/559
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 43 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 13 = 559.
Working: LCD(43, 13) = 559

Step 2: Convert to Equivalent Fractions with Common Denominator 559
Multiply the numerator and denominator of 3/43 by 13, and multiply the numerator and denominator of 4/13 by 43 so both fractions share the common base 559.
Working: 3 × 13/43 × 13 = 39/559 and 4 × 43/13 × 43 = 172/559

Step 3: Add the Numerators
Now add the numerators (39 + 172 = 211) and keep the common denominator 559 unchanged.
Working: 39 + 172/559 = 211/559

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 211 and 559 is 1, confirming that 211/559 cannot be reduced further—it is already in its simplest irreducible form.
Working: 211/559

Step 5: Decimal & Percentage Representation
Dividing the numerator 211 by denominator 559 produces a repeating decimal (approximately 0.37746, or 37.746%).
Working: 211 ÷ 559 = 0.37746 (37.746%)

Key Values:
- Simplified Fraction: 211/559
- Mixed Number Form: 211/559
- Decimal Value: 0.37746
- Percentage: 37.746%

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Solved with FractionsCalc:
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3/43 + 4/13 = 211/559

Simplified Fraction

211/559

Mixed Number

Proper (211/559)

Decimal Value

0.37746

Percentage

37.746%

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Step-by-Step Solution: 3/43 + 4/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 43 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 13 = 559.

LCD(43, 13) = 559

Step 2

Convert to Equivalent Fractions with Common Denominator 559

Multiply the numerator and denominator of 3/43 by 13, and multiply the numerator and denominator of 4/13 by 43 so both fractions share the common base 559.

3 × 13/43 × 13 = 39/559 and 4 × 43/13 × 43 = 172/559

Step 3

Add the Numerators

Now add the numerators (39 + 172 = 211) and keep the common denominator 559 unchanged.

39 + 172/559 = 211/559

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 211 and 559 is 1, confirming that 211/559 cannot be reduced further—it is already in its simplest irreducible form.

211/559

Step 5

Decimal & Percentage Representation

Dividing the numerator 211 by denominator 559 produces a repeating decimal (approximately 0.37746, or 37.746%).

211 ÷ 559 = 0.37746 (37.746%)

Visual Representation

The diagram below illustrates 3/43 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`211/559`
Mixed Number Form	`211/559`
Decimal Form	`0.37746`
Percentage	`37.746%`

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Frequently Asked Questions

What is 3/43 plus 4/13 as a fraction?

3/43 + 4/13 in simplest fraction form is 211/559.

What is 3/43 plus 4/13 as a decimal?

3/43 + 4/13 converted to a decimal is 0.37746.

What is 3/43 plus 4/13 as a percentage?

3/43 + 4/13 expressed as a percentage is 37.746%.

Does 3/43 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.37746...) because the denominator contains prime factors other than 2 and 5.