What is 5/32 plus 2/9? (Answer: 109/288)

Exact Answer

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Problem: What is 5/32 plus 2/9?
Formula / Expression: 5/32 + 2/9
Final Answer: 109/288
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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 5/32 by 9, and multiply the numerator and denominator of 2/9 by 32 so both fractions share the common base 288.
Working: 5 × 9/32 × 9 = 45/288 and 2 × 32/9 × 32 = 64/288

Step 3: Add the Numerators
Now add the numerators (45 + 64 = 109) and keep the common denominator 288 unchanged.
Working: 45 + 64/288 = 109/288

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 288 is 1, confirming that 109/288 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/288

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 288 produces a repeating decimal (approximately 0.378472, or 37.8472%).
Working: 109 ÷ 288 = 0.378472 (37.8472%)

Key Values:
- Simplified Fraction: 109/288
- Mixed Number Form: 109/288
- Decimal Value: 0.378472
- Percentage: 37.8472%

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Solved with FractionsCalc:
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5/32 + 2/9 = 109/288

Simplified Fraction

109/288

Mixed Number

Proper (109/288)

Decimal Value

0.378472

Percentage

37.8472%

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Step-by-Step Solution: 5/32 + 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 5/32 by 9, and multiply the numerator and denominator of 2/9 by 32 so both fractions share the common base 288.

5 × 9/32 × 9 = 45/288 and 2 × 32/9 × 32 = 64/288

Step 3

Add the Numerators

Now add the numerators (45 + 64 = 109) and keep the common denominator 288 unchanged.

45 + 64/288 = 109/288

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 288 is 1, confirming that 109/288 cannot be reduced further—it is already in its simplest irreducible form.

109/288

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 288 produces a repeating decimal (approximately 0.378472, or 37.8472%).

109 ÷ 288 = 0.378472 (37.8472%)

Visual Representation

The diagram below illustrates 5/32 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/288`
Mixed Number Form	`109/288`
Decimal Form	`0.378472`
Percentage	`37.8472%`

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Frequently Asked Questions

What is 5/32 plus 2/9 as a fraction?

5/32 + 2/9 in simplest fraction form is 109/288.

What is 5/32 plus 2/9 as a decimal?

5/32 + 2/9 converted to a decimal is 0.378472.

What is 5/32 plus 2/9 as a percentage?

5/32 + 2/9 expressed as a percentage is 37.8472%.

Does 5/32 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.378472...) because the denominator contains prime factors other than 2 and 5.