What is 2/9 plus 3/5? (Answer: 37/45)

Exact Answer

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Problem: What is 2/9 plus 3/5?
Formula / Expression: 2/9 + 3/5
Final Answer: 37/45
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 5 = 45.
Working: LCD(9, 5) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 2/9 by 5, and multiply the numerator and denominator of 3/5 by 9 so both fractions share the common base 45.
Working: 2 × 5/9 × 5 = 10/45 and 3 × 9/5 × 9 = 27/45

Step 3: Add the Numerators
Now add the numerators (10 + 27 = 37) and keep the common denominator 45 unchanged.
Working: 10 + 27/45 = 37/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 45 is 1, confirming that 37/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 45 produces a repeating decimal (approximately 0.822222, or 82.2222%).
Working: 37 ÷ 45 = 0.822222 (82.2222%)

Key Values:
- Simplified Fraction: 37/45
- Mixed Number Form: 37/45
- Decimal Value: 0.822222
- Percentage: 82.2222%

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Solved with FractionsCalc:
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2/9 + 3/5 = 37/45

Simplified Fraction

37/45

Mixed Number

Proper (37/45)

Decimal Value

0.822222

Percentage

82.2222%

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Step-by-Step Solution: 2/9 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 5 = 45.

LCD(9, 5) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 2/9 by 5, and multiply the numerator and denominator of 3/5 by 9 so both fractions share the common base 45.

2 × 5/9 × 5 = 10/45 and 3 × 9/5 × 9 = 27/45

Step 3

Add the Numerators

Now add the numerators (10 + 27 = 37) and keep the common denominator 45 unchanged.

10 + 27/45 = 37/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 45 is 1, confirming that 37/45 cannot be reduced further—it is already in its simplest irreducible form.

37/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 45 produces a repeating decimal (approximately 0.822222, or 82.2222%).

37 ÷ 45 = 0.822222 (82.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/45`
Mixed Number Form	`37/45`
Decimal Form	`0.822222`
Percentage	`82.2222%`

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Frequently Asked Questions

What is 2/9 plus 3/5 as a fraction?

2/9 + 3/5 in simplest fraction form is 37/45.

What is 2/9 plus 3/5 as a decimal?

2/9 + 3/5 converted to a decimal is 0.822222.

What is 2/9 plus 3/5 as a percentage?

2/9 + 3/5 expressed as a percentage is 82.2222%.

Does 2/9 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.822222...) because the denominator contains prime factors other than 2 and 5.