What is 2/9 plus 9/37? (Answer: 155/333)

Exact Answer

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Problem: What is 2/9 plus 9/37?
Formula / Expression: 2/9 + 9/37
Final Answer: 155/333
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 37 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 37 = 333.
Working: LCD(9, 37) = 333

Step 2: Convert to Equivalent Fractions with Common Denominator 333
Multiply the numerator and denominator of 2/9 by 37, and multiply the numerator and denominator of 9/37 by 9 so both fractions share the common base 333.
Working: 2 × 37/9 × 37 = 74/333 and 9 × 9/37 × 9 = 81/333

Step 3: Add the Numerators
Now add the numerators (74 + 81 = 155) and keep the common denominator 333 unchanged.
Working: 74 + 81/333 = 155/333

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 155 and 333 is 1, confirming that 155/333 cannot be reduced further—it is already in its simplest irreducible form.
Working: 155/333

Step 5: Decimal & Percentage Representation
Dividing the numerator 155 by denominator 333 produces a repeating decimal (approximately 0.465465, or 46.5465%).
Working: 155 ÷ 333 = 0.465465 (46.5465%)

Key Values:
- Simplified Fraction: 155/333
- Mixed Number Form: 155/333
- Decimal Value: 0.465465
- Percentage: 46.5465%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-9-37/
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2/9 + 9/37 = 155/333

Simplified Fraction

155/333

Mixed Number

Proper (155/333)

Decimal Value

0.465465

Percentage

46.5465%

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Step-by-Step Solution: 2/9 + 9/37

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 37 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 37 = 333.

LCD(9, 37) = 333

Step 2

Convert to Equivalent Fractions with Common Denominator 333

Multiply the numerator and denominator of 2/9 by 37, and multiply the numerator and denominator of 9/37 by 9 so both fractions share the common base 333.

2 × 37/9 × 37 = 74/333 and 9 × 9/37 × 9 = 81/333

Step 3

Add the Numerators

Now add the numerators (74 + 81 = 155) and keep the common denominator 333 unchanged.

74 + 81/333 = 155/333

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 155 and 333 is 1, confirming that 155/333 cannot be reduced further—it is already in its simplest irreducible form.

155/333

Step 5

Decimal & Percentage Representation

Dividing the numerator 155 by denominator 333 produces a repeating decimal (approximately 0.465465, or 46.5465%).

155 ÷ 333 = 0.465465 (46.5465%)

Visual Representation

The diagram below illustrates 2/9 plus 9/37 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`155/333`
Mixed Number Form	`155/333`
Decimal Form	`0.465465`
Percentage	`46.5465%`

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Frequently Asked Questions

What is 2/9 plus 9/37 as a fraction?

2/9 + 9/37 in simplest fraction form is 155/333.

What is 2/9 plus 9/37 as a decimal?

2/9 + 9/37 converted to a decimal is 0.465465.

What is 2/9 plus 9/37 as a percentage?

2/9 + 9/37 expressed as a percentage is 46.5465%.

Does 2/9 plus 9/37 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.465465...) because the denominator contains prime factors other than 2 and 5.