What is 1/9 plus 8/21? (Answer: 31/63)

Exact Answer

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Problem: What is 1/9 plus 8/21?
Formula / Expression: 1/9 + 8/21
Final Answer: 31/63
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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 1/9 by 7, and multiply the numerator and denominator of 8/21 by 3 so both fractions share the common base 63.
Working: 1 × 7/9 × 7 = 7/63 and 8 × 3/21 × 3 = 24/63

Step 3: Add the Numerators
Now add the numerators (7 + 24 = 31) and keep the common denominator 63 unchanged.
Working: 7 + 24/63 = 31/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 63 is 1, confirming that 31/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 63 produces a repeating decimal (approximately 0.492063, or 49.2063%).
Working: 31 ÷ 63 = 0.492063 (49.2063%)

Key Values:
- Simplified Fraction: 31/63
- Mixed Number Form: 31/63
- Decimal Value: 0.492063
- Percentage: 49.2063%

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Solved with FractionsCalc:
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1/9 + 8/21 = 31/63

Simplified Fraction

31/63

Mixed Number

Proper (31/63)

Decimal Value

0.492063

Percentage

49.2063%

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Step-by-Step Solution: 1/9 + 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 1/9 by 7, and multiply the numerator and denominator of 8/21 by 3 so both fractions share the common base 63.

1 × 7/9 × 7 = 7/63 and 8 × 3/21 × 3 = 24/63

Step 3

Add the Numerators

Now add the numerators (7 + 24 = 31) and keep the common denominator 63 unchanged.

7 + 24/63 = 31/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 63 is 1, confirming that 31/63 cannot be reduced further—it is already in its simplest irreducible form.

31/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 63 produces a repeating decimal (approximately 0.492063, or 49.2063%).

31 ÷ 63 = 0.492063 (49.2063%)

Visual Representation

The diagram below illustrates 1/9 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/63`
Mixed Number Form	`31/63`
Decimal Form	`0.492063`
Percentage	`49.2063%`

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Frequently Asked Questions

What is 1/9 plus 8/21 as a fraction?

1/9 + 8/21 in simplest fraction form is 31/63.

What is 1/9 plus 8/21 as a decimal?

1/9 + 8/21 converted to a decimal is 0.492063.

What is 1/9 plus 8/21 as a percentage?

1/9 + 8/21 expressed as a percentage is 49.2063%.

Does 1/9 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.492063...) because the denominator contains prime factors other than 2 and 5.