What is 2/32 plus 2/9? (Answer: 41/144)

Exact Answer

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Problem: What is 2/32 plus 2/9?
Formula / Expression: 2/32 + 2/9
Final Answer: 41/144
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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 2/9 by 32 so both fractions share the common base 288.
Working: 2 × 9/32 × 9 = 18/288 and 2 × 32/9 × 32 = 64/288

Step 3: Add the Numerators
Now add the numerators (18 + 64 = 82) and keep the common denominator 288 unchanged.
Working: 18 + 64/288 = 82/288

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 288, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/288 ÷ 2 = 41/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 144 produces a repeating decimal (approximately 0.284722, or 28.4722%).
Working: 41 ÷ 144 = 0.284722 (28.4722%)

Key Values:
- Simplified Fraction: 41/144
- Mixed Number Form: 41/144
- Decimal Value: 0.284722
- Percentage: 28.4722%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-32-plus-2-9/
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2/32 + 2/9 = 41/144

Simplified Fraction

41/144

Mixed Number

Proper (41/144)

Decimal Value

0.284722

Percentage

28.4722%

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

2 × 9/32 × 9 = 18/288 and 2 × 32/9 × 32 = 64/288

Step 3

Add the Numerators

Now add the numerators (18 + 64 = 82) and keep the common denominator 288 unchanged.

18 + 64/288 = 82/288

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 288, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/288 ÷ 2 = 41/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 144 produces a repeating decimal (approximately 0.284722, or 28.4722%).

41 ÷ 144 = 0.284722 (28.4722%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/144`
Mixed Number Form	`41/144`
Decimal Form	`0.284722`
Percentage	`28.4722%`

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Frequently Asked Questions

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

2/32 + 2/9 in simplest fraction form is 41/144.

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

2/32 + 2/9 converted to a decimal is 0.284722.

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

2/32 + 2/9 expressed as a percentage is 28.4722%.

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

It results in a repeating decimal (approximately 0.284722...) because the denominator contains prime factors other than 2 and 5.