What is 3/21 plus 2/9? (Answer: 23/63)

Exact Answer

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Problem: What is 3/21 plus 2/9?
Formula / Expression: 3/21 + 2/9
Final Answer: 23/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).
Working: LCD(21, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 3/21 by 3, and multiply the numerator and denominator of 2/9 by 7 so both fractions share the common base 63.
Working: 3 × 3/21 × 3 = 9/63 and 2 × 7/9 × 7 = 14/63

Step 3: Add the Numerators
Now add the numerators (9 + 14 = 23) and keep the common denominator 63 unchanged.
Working: 9 + 14/63 = 23/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 63 is 1, confirming that 23/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 63 produces a repeating decimal (approximately 0.365079, or 36.5079%).
Working: 23 ÷ 63 = 0.365079 (36.5079%)

Key Values:
- Simplified Fraction: 23/63
- Mixed Number Form: 23/63
- Decimal Value: 0.365079
- Percentage: 36.5079%

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Solved with FractionsCalc:
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3/21 + 2/9 = 23/63

Simplified Fraction

23/63

Mixed Number

Proper (23/63)

Decimal Value

0.365079

Percentage

36.5079%

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Step-by-Step Solution: 3/21 + 2/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 3/21 by 3, and multiply the numerator and denominator of 2/9 by 7 so both fractions share the common base 63.

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

Step 3

Add the Numerators

Now add the numerators (9 + 14 = 23) and keep the common denominator 63 unchanged.

9 + 14/63 = 23/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 63 is 1, confirming that 23/63 cannot be reduced further—it is already in its simplest irreducible form.

23/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 63 produces a repeating decimal (approximately 0.365079, or 36.5079%).

23 ÷ 63 = 0.365079 (36.5079%)

Visual Representation

The diagram below illustrates 3/21 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/63`
Mixed Number Form	`23/63`
Decimal Form	`0.365079`
Percentage	`36.5079%`

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Frequently Asked Questions

What is 3/21 plus 2/9 as a fraction?

3/21 + 2/9 in simplest fraction form is 23/63.

What is 3/21 plus 2/9 as a decimal?

3/21 + 2/9 converted to a decimal is 0.365079.

What is 3/21 plus 2/9 as a percentage?

3/21 + 2/9 expressed as a percentage is 36.5079%.

Does 3/21 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.365079...) because the denominator contains prime factors other than 2 and 5.