What is 4/32 plus 2/9? (Answer: 25/72)

Exact Answer

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Problem: What is 4/32 plus 2/9?
Formula / Expression: 4/32 + 2/9
Final Answer: 25/72
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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 4/32 by 9, and multiply the numerator and denominator of 2/9 by 32 so both fractions share the common base 288.
Working: 4 × 9/32 × 9 = 36/288 and 2 × 32/9 × 32 = 64/288

Step 3: Add the Numerators
Now add the numerators (36 + 64 = 100) and keep the common denominator 288 unchanged.
Working: 36 + 64/288 = 100/288

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 100 and 288, which is 4. Divide both the numerator and denominator by 4.
Working: 100 ÷ 4/288 ÷ 4 = 25/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 72 produces a repeating decimal (approximately 0.347222, or 34.7222%).
Working: 25 ÷ 72 = 0.347222 (34.7222%)

Key Values:
- Simplified Fraction: 25/72
- Mixed Number Form: 25/72
- Decimal Value: 0.347222
- Percentage: 34.7222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-32-plus-2-9/
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4/32 + 2/9 = 25/72

Simplified Fraction

25/72

Mixed Number

Proper (25/72)

Decimal Value

0.347222

Percentage

34.7222%

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Step-by-Step Solution: 4/32 + 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 4/32 by 9, and multiply the numerator and denominator of 2/9 by 32 so both fractions share the common base 288.

4 × 9/32 × 9 = 36/288 and 2 × 32/9 × 32 = 64/288

Step 3

Add the Numerators

Now add the numerators (36 + 64 = 100) and keep the common denominator 288 unchanged.

36 + 64/288 = 100/288

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 100 and 288, which is 4. Divide both the numerator and denominator by 4.

100 ÷ 4/288 ÷ 4 = 25/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 72 produces a repeating decimal (approximately 0.347222, or 34.7222%).

25 ÷ 72 = 0.347222 (34.7222%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/72`
Mixed Number Form	`25/72`
Decimal Form	`0.347222`
Percentage	`34.7222%`

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Frequently Asked Questions

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

4/32 + 2/9 in simplest fraction form is 25/72.

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

4/32 + 2/9 converted to a decimal is 0.347222.

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

4/32 + 2/9 expressed as a percentage is 34.7222%.

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

It results in a repeating decimal (approximately 0.347222...) because the denominator contains prime factors other than 2 and 5.