What is 2/9 plus 8/21? (Answer: 38/63)

Exact Answer

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Problem: What is 2/9 plus 8/21?
Formula / Expression: 2/9 + 8/21
Final Answer: 38/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 9 × 21 = 189, keeping the calculation simpler).
Working: LCD(9, 21) = 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 8/21 by 3 so both fractions share the common base 63.
Working: 2 × 7/9 × 7 = 14/63 and 8 × 3/21 × 3 = 24/63

Step 3: Add the Numerators
Now add the numerators (14 + 24 = 38) and keep the common denominator 63 unchanged.
Working: 14 + 24/63 = 38/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 38 and 63 is 1, confirming that 38/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 38/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 63 produces a repeating decimal (approximately 0.603175, or 60.3175%).
Working: 38 ÷ 63 = 0.603175 (60.3175%)

Key Values:
- Simplified Fraction: 38/63
- Mixed Number Form: 38/63
- Decimal Value: 0.603175
- Percentage: 60.3175%

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Solved with FractionsCalc:
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2/9 + 8/21 = 38/63

Simplified Fraction

38/63

Mixed Number

Proper (38/63)

Decimal Value

0.603175

Percentage

60.3175%

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Step-by-Step Solution: 2/9 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 9 × 21 = 189, keeping the calculation simpler).

LCD(9, 21) = 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 8/21 by 3 so both fractions share the common base 63.

2 × 7/9 × 7 = 14/63 and 8 × 3/21 × 3 = 24/63

Step 3

Add the Numerators

Now add the numerators (14 + 24 = 38) and keep the common denominator 63 unchanged.

14 + 24/63 = 38/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 38 and 63 is 1, confirming that 38/63 cannot be reduced further—it is already in its simplest irreducible form.

38/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 63 produces a repeating decimal (approximately 0.603175, or 60.3175%).

38 ÷ 63 = 0.603175 (60.3175%)

Visual Representation

The diagram below illustrates 2/9 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/63`
Mixed Number Form	`38/63`
Decimal Form	`0.603175`
Percentage	`60.3175%`

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Frequently Asked Questions

What is 2/9 plus 8/21 as a fraction?

2/9 + 8/21 in simplest fraction form is 38/63.

What is 2/9 plus 8/21 as a decimal?

2/9 + 8/21 converted to a decimal is 0.603175.

What is 2/9 plus 8/21 as a percentage?

2/9 + 8/21 expressed as a percentage is 60.3175%.

Does 2/9 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.603175...) because the denominator contains prime factors other than 2 and 5.