What is 2/9 plus 5/21? (Answer: 29/63)

Exact Answer

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Problem: What is 2/9 plus 5/21?
Formula / Expression: 2/9 + 5/21
Final Answer: 29/63
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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 5/21 by 3 so both fractions share the common base 63.
Working: 2 × 7/9 × 7 = 14/63 and 5 × 3/21 × 3 = 15/63

Step 3: Add the Numerators
Now add the numerators (14 + 15 = 29) and keep the common denominator 63 unchanged.
Working: 14 + 15/63 = 29/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 63 is 1, confirming that 29/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 63 produces a repeating decimal (approximately 0.460317, or 46.0317%).
Working: 29 ÷ 63 = 0.460317 (46.0317%)

Key Values:
- Simplified Fraction: 29/63
- Mixed Number Form: 29/63
- Decimal Value: 0.460317
- Percentage: 46.0317%

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Solved with FractionsCalc:
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2/9 + 5/21 = 29/63

Simplified Fraction

29/63

Mixed Number

Proper (29/63)

Decimal Value

0.460317

Percentage

46.0317%

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Step-by-Step Solution: 2/9 + 5/21

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 5/21 by 3 so both fractions share the common base 63.

2 × 7/9 × 7 = 14/63 and 5 × 3/21 × 3 = 15/63

Step 3

Add the Numerators

Now add the numerators (14 + 15 = 29) and keep the common denominator 63 unchanged.

14 + 15/63 = 29/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 63 is 1, confirming that 29/63 cannot be reduced further—it is already in its simplest irreducible form.

29/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 63 produces a repeating decimal (approximately 0.460317, or 46.0317%).

29 ÷ 63 = 0.460317 (46.0317%)

Visual Representation

The diagram below illustrates 2/9 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/63`
Mixed Number Form	`29/63`
Decimal Form	`0.460317`
Percentage	`46.0317%`

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Frequently Asked Questions

What is 2/9 plus 5/21 as a fraction?

2/9 + 5/21 in simplest fraction form is 29/63.

What is 2/9 plus 5/21 as a decimal?

2/9 + 5/21 converted to a decimal is 0.460317.

What is 2/9 plus 5/21 as a percentage?

2/9 + 5/21 expressed as a percentage is 46.0317%.

Does 2/9 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.460317...) because the denominator contains prime factors other than 2 and 5.