What is 2/32 plus 3/9? (Answer: 19/48)

Exact Answer

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Problem: What is 2/32 plus 3/9?
Formula / Expression: 2/32 + 3/9
Final Answer: 19/48
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 9 = 288.
Working: LCD(32, 9) = 288

Step 2: Convert to Equivalent Fractions with Common Denominator 288
Multiply the numerator and denominator of 2/32 by 9, and multiply the numerator and denominator of 3/9 by 32 so both fractions share the common base 288.
Working: 2 × 9/32 × 9 = 18/288 and 3 × 32/9 × 32 = 96/288

Step 3: Add the Numerators
Now add the numerators (18 + 96 = 114) and keep the common denominator 288 unchanged.
Working: 18 + 96/288 = 114/288

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 288, which is 6. Divide both the numerator and denominator by 6.
Working: 114 ÷ 6/288 ÷ 6 = 19/48

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 48 produces a repeating decimal (approximately 0.395833, or 39.5833%).
Working: 19 ÷ 48 = 0.395833 (39.5833%)

Key Values:
- Simplified Fraction: 19/48
- Mixed Number Form: 19/48
- Decimal Value: 0.395833
- Percentage: 39.5833%

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Solved with FractionsCalc:
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2/32 + 3/9 = 19/48

Simplified Fraction

19/48

Mixed Number

Proper (19/48)

Decimal Value

0.395833

Percentage

39.5833%

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Step-by-Step Solution: 2/32 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 9 = 288.

LCD(32, 9) = 288

Step 2

Convert to Equivalent Fractions with Common Denominator 288

Multiply the numerator and denominator of 2/32 by 9, and multiply the numerator and denominator of 3/9 by 32 so both fractions share the common base 288.

2 × 9/32 × 9 = 18/288 and 3 × 32/9 × 32 = 96/288

Step 3

Add the Numerators

Now add the numerators (18 + 96 = 114) and keep the common denominator 288 unchanged.

18 + 96/288 = 114/288

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 288, which is 6. Divide both the numerator and denominator by 6.

114 ÷ 6/288 ÷ 6 = 19/48

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 48 produces a repeating decimal (approximately 0.395833, or 39.5833%).

19 ÷ 48 = 0.395833 (39.5833%)

Visual Representation

The diagram below illustrates 2/32 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/48`
Mixed Number Form	`19/48`
Decimal Form	`0.395833`
Percentage	`39.5833%`

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Frequently Asked Questions

What is 2/32 plus 3/9 as a fraction?

2/32 + 3/9 in simplest fraction form is 19/48.

What is 2/32 plus 3/9 as a decimal?

2/32 + 3/9 converted to a decimal is 0.395833.

What is 2/32 plus 3/9 as a percentage?

2/32 + 3/9 expressed as a percentage is 39.5833%.

Does 2/32 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.395833...) because the denominator contains prime factors other than 2 and 5.