What is 3/32 plus 2/9? (Answer: 91/288)

Exact Answer

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Problem: What is 3/32 plus 2/9?
Formula / Expression: 3/32 + 2/9
Final Answer: 91/288
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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 3/32 by 9, and multiply the numerator and denominator of 2/9 by 32 so both fractions share the common base 288.
Working: 3 × 9/32 × 9 = 27/288 and 2 × 32/9 × 32 = 64/288

Step 3: Add the Numerators
Now add the numerators (27 + 64 = 91) and keep the common denominator 288 unchanged.
Working: 27 + 64/288 = 91/288

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 91 and 288 is 1, confirming that 91/288 cannot be reduced further—it is already in its simplest irreducible form.
Working: 91/288

Step 5: Decimal & Percentage Representation
Dividing the numerator 91 by denominator 288 produces a repeating decimal (approximately 0.315972, or 31.5972%).
Working: 91 ÷ 288 = 0.315972 (31.5972%)

Key Values:
- Simplified Fraction: 91/288
- Mixed Number Form: 91/288
- Decimal Value: 0.315972
- Percentage: 31.5972%

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Solved with FractionsCalc:
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3/32 + 2/9 = 91/288

Simplified Fraction

91/288

Mixed Number

Proper (91/288)

Decimal Value

0.315972

Percentage

31.5972%

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

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

3 × 9/32 × 9 = 27/288 and 2 × 32/9 × 32 = 64/288

Step 3

Add the Numerators

Now add the numerators (27 + 64 = 91) and keep the common denominator 288 unchanged.

27 + 64/288 = 91/288

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 91 and 288 is 1, confirming that 91/288 cannot be reduced further—it is already in its simplest irreducible form.

91/288

Step 5

Decimal & Percentage Representation

Dividing the numerator 91 by denominator 288 produces a repeating decimal (approximately 0.315972, or 31.5972%).

91 ÷ 288 = 0.315972 (31.5972%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`91/288`
Mixed Number Form	`91/288`
Decimal Form	`0.315972`
Percentage	`31.5972%`

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Frequently Asked Questions

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

3/32 + 2/9 in simplest fraction form is 91/288.

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

3/32 + 2/9 converted to a decimal is 0.315972.

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

3/32 + 2/9 expressed as a percentage is 31.5972%.

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

It results in a repeating decimal (approximately 0.315972...) because the denominator contains prime factors other than 2 and 5.