What is 2/21 plus 5/9? (Answer: 41/63)

Exact Answer

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Problem: What is 2/21 plus 5/9?
Formula / Expression: 2/21 + 5/9
Final Answer: 41/63
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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 2/21 by 3, and multiply the numerator and denominator of 5/9 by 7 so both fractions share the common base 63.
Working: 2 × 3/21 × 3 = 6/63 and 5 × 7/9 × 7 = 35/63

Step 3: Add the Numerators
Now add the numerators (6 + 35 = 41) and keep the common denominator 63 unchanged.
Working: 6 + 35/63 = 41/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 63 is 1, confirming that 41/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).
Working: 41 ÷ 63 = 0.650794 (65.0794%)

Key Values:
- Simplified Fraction: 41/63
- Mixed Number Form: 41/63
- Decimal Value: 0.650794
- Percentage: 65.0794%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-5-9/
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2/21 + 5/9 = 41/63

Simplified Fraction

41/63

Mixed Number

Proper (41/63)

Decimal Value

0.650794

Percentage

65.0794%

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

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 2/21 by 3, and multiply the numerator and denominator of 5/9 by 7 so both fractions share the common base 63.

2 × 3/21 × 3 = 6/63 and 5 × 7/9 × 7 = 35/63

Step 3

Add the Numerators

Now add the numerators (6 + 35 = 41) and keep the common denominator 63 unchanged.

6 + 35/63 = 41/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 63 is 1, confirming that 41/63 cannot be reduced further—it is already in its simplest irreducible form.

41/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).

41 ÷ 63 = 0.650794 (65.0794%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/63`
Mixed Number Form	`41/63`
Decimal Form	`0.650794`
Percentage	`65.0794%`

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Frequently Asked Questions

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

2/21 + 5/9 in simplest fraction form is 41/63.

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

2/21 + 5/9 converted to a decimal is 0.650794.

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

2/21 + 5/9 expressed as a percentage is 65.0794%.

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

It results in a repeating decimal (approximately 0.650794...) because the denominator contains prime factors other than 2 and 5.