What is 2/32 plus 2/13? (Answer: 45/208)

Exact Answer

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Problem: What is 2/32 plus 2/13?
Formula / Expression: 2/32 + 2/13
Final Answer: 45/208
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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 2/32 by 13, and multiply the numerator and denominator of 2/13 by 32 so both fractions share the common base 416.
Working: 2 × 13/32 × 13 = 26/416 and 2 × 32/13 × 32 = 64/416

Step 3: Add the Numerators
Now add the numerators (26 + 64 = 90) and keep the common denominator 416 unchanged.
Working: 26 + 64/416 = 90/416

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 416, which is 2. Divide both the numerator and denominator by 2.
Working: 90 ÷ 2/416 ÷ 2 = 45/208

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 208 produces a repeating decimal (approximately 0.216346, or 21.6346%).
Working: 45 ÷ 208 = 0.216346 (21.6346%)

Key Values:
- Simplified Fraction: 45/208
- Mixed Number Form: 45/208
- Decimal Value: 0.216346
- Percentage: 21.6346%

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Solved with FractionsCalc:
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2/32 + 2/13 = 45/208

Simplified Fraction

45/208

Mixed Number

Proper (45/208)

Decimal Value

0.216346

Percentage

21.6346%

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Step-by-Step Solution: 2/32 + 2/13

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 2/32 by 13, and multiply the numerator and denominator of 2/13 by 32 so both fractions share the common base 416.

2 × 13/32 × 13 = 26/416 and 2 × 32/13 × 32 = 64/416

Step 3

Add the Numerators

Now add the numerators (26 + 64 = 90) and keep the common denominator 416 unchanged.

26 + 64/416 = 90/416

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 416, which is 2. Divide both the numerator and denominator by 2.

90 ÷ 2/416 ÷ 2 = 45/208

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 208 produces a repeating decimal (approximately 0.216346, or 21.6346%).

45 ÷ 208 = 0.216346 (21.6346%)

Visual Representation

The diagram below illustrates 2/32 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/208`
Mixed Number Form	`45/208`
Decimal Form	`0.216346`
Percentage	`21.6346%`

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Frequently Asked Questions

What is 2/32 plus 2/13 as a fraction?

2/32 + 2/13 in simplest fraction form is 45/208.

What is 2/32 plus 2/13 as a decimal?

2/32 + 2/13 converted to a decimal is 0.216346.

What is 2/32 plus 2/13 as a percentage?

2/32 + 2/13 expressed as a percentage is 21.6346%.

Does 2/32 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.216346...) because the denominator contains prime factors other than 2 and 5.