What is 3/32 plus 5/13? (Answer: 199/416)

Exact Answer

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Problem: What is 3/32 plus 5/13?
Formula / Expression: 3/32 + 5/13
Final Answer: 199/416
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.
Working: LCD(32, 13) = 416

Step 2: Convert to Equivalent Fractions with Common Denominator 416
Multiply the numerator and denominator of 3/32 by 13, and multiply the numerator and denominator of 5/13 by 32 so both fractions share the common base 416.
Working: 3 × 13/32 × 13 = 39/416 and 5 × 32/13 × 32 = 160/416

Step 3: Add the Numerators
Now add the numerators (39 + 160 = 199) and keep the common denominator 416 unchanged.
Working: 39 + 160/416 = 199/416

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 199 and 416 is 1, confirming that 199/416 cannot be reduced further—it is already in its simplest irreducible form.
Working: 199/416

Step 5: Decimal & Percentage Representation
Dividing the numerator 199 by denominator 416 produces a repeating decimal (approximately 0.478365, or 47.8365%).
Working: 199 ÷ 416 = 0.478365 (47.8365%)

Key Values:
- Simplified Fraction: 199/416
- Mixed Number Form: 199/416
- Decimal Value: 0.478365
- Percentage: 47.8365%

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Solved with FractionsCalc:
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3/32 + 5/13 = 199/416

Simplified Fraction

199/416

Mixed Number

Proper (199/416)

Decimal Value

0.478365

Percentage

47.8365%

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Step-by-Step Solution: 3/32 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.

LCD(32, 13) = 416

Step 2

Convert to Equivalent Fractions with Common Denominator 416

Multiply the numerator and denominator of 3/32 by 13, and multiply the numerator and denominator of 5/13 by 32 so both fractions share the common base 416.

3 × 13/32 × 13 = 39/416 and 5 × 32/13 × 32 = 160/416

Step 3

Add the Numerators

Now add the numerators (39 + 160 = 199) and keep the common denominator 416 unchanged.

39 + 160/416 = 199/416

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 199 and 416 is 1, confirming that 199/416 cannot be reduced further—it is already in its simplest irreducible form.

199/416

Step 5

Decimal & Percentage Representation

Dividing the numerator 199 by denominator 416 produces a repeating decimal (approximately 0.478365, or 47.8365%).

199 ÷ 416 = 0.478365 (47.8365%)

Visual Representation

The diagram below illustrates 3/32 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`199/416`
Mixed Number Form	`199/416`
Decimal Form	`0.478365`
Percentage	`47.8365%`

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Frequently Asked Questions

What is 3/32 plus 5/13 as a fraction?

3/32 + 5/13 in simplest fraction form is 199/416.

What is 3/32 plus 5/13 as a decimal?

3/32 + 5/13 converted to a decimal is 0.478365.

What is 3/32 plus 5/13 as a percentage?

3/32 + 5/13 expressed as a percentage is 47.8365%.

Does 3/32 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.478365...) because the denominator contains prime factors other than 2 and 5.