What is 8/37 plus 2/9? (Answer: 146/333)

Exact Answer

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Problem: What is 8/37 plus 2/9?
Formula / Expression: 8/37 + 2/9
Final Answer: 146/333
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 333
Multiply the numerator and denominator of 8/37 by 9, and multiply the numerator and denominator of 2/9 by 37 so both fractions share the common base 333.
Working: 8 × 9/37 × 9 = 72/333 and 2 × 37/9 × 37 = 74/333

Step 3: Add the Numerators
Now add the numerators (72 + 74 = 146) and keep the common denominator 333 unchanged.
Working: 72 + 74/333 = 146/333

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 146 and 333 is 1, confirming that 146/333 cannot be reduced further—it is already in its simplest irreducible form.
Working: 146/333

Step 5: Decimal & Percentage Representation
Dividing the numerator 146 by denominator 333 produces a repeating decimal (approximately 0.438438, or 43.8438%).
Working: 146 ÷ 333 = 0.438438 (43.8438%)

Key Values:
- Simplified Fraction: 146/333
- Mixed Number Form: 146/333
- Decimal Value: 0.438438
- Percentage: 43.8438%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-37-plus-2-9/
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8/37 + 2/9 = 146/333

Simplified Fraction

146/333

Mixed Number

Proper (146/333)

Decimal Value

0.438438

Percentage

43.8438%

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Step-by-Step Solution: 8/37 + 2/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(37, 9) = 333

Step 2

Convert to Equivalent Fractions with Common Denominator 333

Multiply the numerator and denominator of 8/37 by 9, and multiply the numerator and denominator of 2/9 by 37 so both fractions share the common base 333.

8 × 9/37 × 9 = 72/333 and 2 × 37/9 × 37 = 74/333

Step 3

Add the Numerators

Now add the numerators (72 + 74 = 146) and keep the common denominator 333 unchanged.

72 + 74/333 = 146/333

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 146 and 333 is 1, confirming that 146/333 cannot be reduced further—it is already in its simplest irreducible form.

146/333

Step 5

Decimal & Percentage Representation

Dividing the numerator 146 by denominator 333 produces a repeating decimal (approximately 0.438438, or 43.8438%).

146 ÷ 333 = 0.438438 (43.8438%)

Visual Representation

The diagram below illustrates 8/37 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`146/333`
Mixed Number Form	`146/333`
Decimal Form	`0.438438`
Percentage	`43.8438%`

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Frequently Asked Questions

What is 8/37 plus 2/9 as a fraction?

8/37 + 2/9 in simplest fraction form is 146/333.

What is 8/37 plus 2/9 as a decimal?

8/37 + 2/9 converted to a decimal is 0.438438.

What is 8/37 plus 2/9 as a percentage?

8/37 + 2/9 expressed as a percentage is 43.8438%.

Does 8/37 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.438438...) because the denominator contains prime factors other than 2 and 5.