What is 2/9 plus 2/7? (Answer: 32/63)

Exact Answer

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Problem: What is 2/9 plus 2/7?
Formula / Expression: 2/9 + 2/7
Final Answer: 32/63
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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 2/7 by 9 so both fractions share the common base 63.
Working: 2 × 7/9 × 7 = 14/63 and 2 × 9/7 × 9 = 18/63

Step 3: Add the Numerators
Now add the numerators (14 + 18 = 32) and keep the common denominator 63 unchanged.
Working: 14 + 18/63 = 32/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 32 and 63 is 1, confirming that 32/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 32/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 63 produces a repeating decimal (approximately 0.507937, or 50.7937%).
Working: 32 ÷ 63 = 0.507937 (50.7937%)

Key Values:
- Simplified Fraction: 32/63
- Mixed Number Form: 32/63
- Decimal Value: 0.507937
- Percentage: 50.7937%

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Solved with FractionsCalc:
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2/9 + 2/7 = 32/63

Simplified Fraction

32/63

Mixed Number

Proper (32/63)

Decimal Value

0.507937

Percentage

50.7937%

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

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 2/7 by 9 so both fractions share the common base 63.

2 × 7/9 × 7 = 14/63 and 2 × 9/7 × 9 = 18/63

Step 3

Add the Numerators

Now add the numerators (14 + 18 = 32) and keep the common denominator 63 unchanged.

14 + 18/63 = 32/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 32 and 63 is 1, confirming that 32/63 cannot be reduced further—it is already in its simplest irreducible form.

32/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 63 produces a repeating decimal (approximately 0.507937, or 50.7937%).

32 ÷ 63 = 0.507937 (50.7937%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/63`
Mixed Number Form	`32/63`
Decimal Form	`0.507937`
Percentage	`50.7937%`

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Frequently Asked Questions

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

2/9 + 2/7 in simplest fraction form is 32/63.

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

2/9 + 2/7 converted to a decimal is 0.507937.

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

2/9 + 2/7 expressed as a percentage is 50.7937%.

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

It results in a repeating decimal (approximately 0.507937...) because the denominator contains prime factors other than 2 and 5.