What is 2/32 plus 5/9? (Answer: 89/144)

Exact Answer

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Problem: What is 2/32 plus 5/9?
Formula / Expression: 2/32 + 5/9
Final Answer: 89/144
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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 5/9 by 32 so both fractions share the common base 288.
Working: 2 × 9/32 × 9 = 18/288 and 5 × 32/9 × 32 = 160/288

Step 3: Add the Numerators
Now add the numerators (18 + 160 = 178) and keep the common denominator 288 unchanged.
Working: 18 + 160/288 = 178/288

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 178 and 288, which is 2. Divide both the numerator and denominator by 2.
Working: 178 ÷ 2/288 ÷ 2 = 89/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 144 produces a repeating decimal (approximately 0.618056, or 61.8056%).
Working: 89 ÷ 144 = 0.618056 (61.8056%)

Key Values:
- Simplified Fraction: 89/144
- Mixed Number Form: 89/144
- Decimal Value: 0.618056
- Percentage: 61.8056%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-32-plus-5-9/
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2/32 + 5/9 = 89/144

Simplified Fraction

89/144

Mixed Number

Proper (89/144)

Decimal Value

0.618056

Percentage

61.8056%

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Step-by-Step Solution: 2/32 + 5/9

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 5/9 by 32 so both fractions share the common base 288.

2 × 9/32 × 9 = 18/288 and 5 × 32/9 × 32 = 160/288

Step 3

Add the Numerators

Now add the numerators (18 + 160 = 178) and keep the common denominator 288 unchanged.

18 + 160/288 = 178/288

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 178 and 288, which is 2. Divide both the numerator and denominator by 2.

178 ÷ 2/288 ÷ 2 = 89/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 144 produces a repeating decimal (approximately 0.618056, or 61.8056%).

89 ÷ 144 = 0.618056 (61.8056%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/144`
Mixed Number Form	`89/144`
Decimal Form	`0.618056`
Percentage	`61.8056%`

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Frequently Asked Questions

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

2/32 + 5/9 in simplest fraction form is 89/144.

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

2/32 + 5/9 converted to a decimal is 0.618056.

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

2/32 + 5/9 expressed as a percentage is 61.8056%.

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

It results in a repeating decimal (approximately 0.618056...) because the denominator contains prime factors other than 2 and 5.