What is 2/9 plus 3/7? (Answer: 41/63)

Exact Answer

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Problem: What is 2/9 plus 3/7?
Formula / Expression: 2/9 + 3/7
Final Answer: 41/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 7 = 63.
Working: LCD(9, 7) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 2/9 by 7, and multiply the numerator and denominator of 3/7 by 9 so both fractions share the common base 63.
Working: 2 × 7/9 × 7 = 14/63 and 3 × 9/7 × 9 = 27/63

Step 3: Add the Numerators
Now add the numerators (14 + 27 = 41) and keep the common denominator 63 unchanged.
Working: 14 + 27/63 = 41/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 63 is 1, confirming that 41/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).
Working: 41 ÷ 63 = 0.650794 (65.0794%)

Key Values:
- Simplified Fraction: 41/63
- Mixed Number Form: 41/63
- Decimal Value: 0.650794
- Percentage: 65.0794%

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Solved with FractionsCalc:
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2/9 + 3/7 = 41/63

Simplified Fraction

41/63

Mixed Number

Proper (41/63)

Decimal Value

0.650794

Percentage

65.0794%

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Step-by-Step Solution: 2/9 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 7 = 63.

LCD(9, 7) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 2/9 by 7, and multiply the numerator and denominator of 3/7 by 9 so both fractions share the common base 63.

2 × 7/9 × 7 = 14/63 and 3 × 9/7 × 9 = 27/63

Step 3

Add the Numerators

Now add the numerators (14 + 27 = 41) and keep the common denominator 63 unchanged.

14 + 27/63 = 41/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 63 is 1, confirming that 41/63 cannot be reduced further—it is already in its simplest irreducible form.

41/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).

41 ÷ 63 = 0.650794 (65.0794%)

Visual Representation

The diagram below illustrates 2/9 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/63`
Mixed Number Form	`41/63`
Decimal Form	`0.650794`
Percentage	`65.0794%`

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Frequently Asked Questions

What is 2/9 plus 3/7 as a fraction?

2/9 + 3/7 in simplest fraction form is 41/63.

What is 2/9 plus 3/7 as a decimal?

2/9 + 3/7 converted to a decimal is 0.650794.

What is 2/9 plus 3/7 as a percentage?

2/9 + 3/7 expressed as a percentage is 65.0794%.

Does 2/9 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.650794...) because the denominator contains prime factors other than 2 and 5.