What is 2/32 plus 4/9? (Answer: 73/144)

Exact Answer

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Problem: What is 2/32 plus 4/9?
Formula / Expression: 2/32 + 4/9
Final Answer: 73/144
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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 4/9 by 32 so both fractions share the common base 288.
Working: 2 × 9/32 × 9 = 18/288 and 4 × 32/9 × 32 = 128/288

Step 3: Add the Numerators
Now add the numerators (18 + 128 = 146) and keep the common denominator 288 unchanged.
Working: 18 + 128/288 = 146/288

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 146 and 288, which is 2. Divide both the numerator and denominator by 2.
Working: 146 ÷ 2/288 ÷ 2 = 73/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 144 produces a repeating decimal (approximately 0.506944, or 50.6944%).
Working: 73 ÷ 144 = 0.506944 (50.6944%)

Key Values:
- Simplified Fraction: 73/144
- Mixed Number Form: 73/144
- Decimal Value: 0.506944
- Percentage: 50.6944%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-32-plus-4-9/
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2/32 + 4/9 = 73/144

Simplified Fraction

73/144

Mixed Number

Proper (73/144)

Decimal Value

0.506944

Percentage

50.6944%

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Step-by-Step Solution: 2/32 + 4/9

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 4/9 by 32 so both fractions share the common base 288.

2 × 9/32 × 9 = 18/288 and 4 × 32/9 × 32 = 128/288

Step 3

Add the Numerators

Now add the numerators (18 + 128 = 146) and keep the common denominator 288 unchanged.

18 + 128/288 = 146/288

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 146 and 288, which is 2. Divide both the numerator and denominator by 2.

146 ÷ 2/288 ÷ 2 = 73/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 144 produces a repeating decimal (approximately 0.506944, or 50.6944%).

73 ÷ 144 = 0.506944 (50.6944%)

Visual Representation

The diagram below illustrates 2/32 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/144`
Mixed Number Form	`73/144`
Decimal Form	`0.506944`
Percentage	`50.6944%`

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Frequently Asked Questions

What is 2/32 plus 4/9 as a fraction?

2/32 + 4/9 in simplest fraction form is 73/144.

What is 2/32 plus 4/9 as a decimal?

2/32 + 4/9 converted to a decimal is 0.506944.

What is 2/32 plus 4/9 as a percentage?

2/32 + 4/9 expressed as a percentage is 50.6944%.

Does 2/32 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.506944...) because the denominator contains prime factors other than 2 and 5.