What is 8/39 plus 9/21? (Answer: 173/273)

Exact Answer

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Problem: What is 8/39 plus 9/21?
Formula / Expression: 8/39 + 9/21
Final Answer: 173/273
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
Working: LCD(39, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 8/39 by 7, and multiply the numerator and denominator of 9/21 by 13 so both fractions share the common base 273.
Working: 8 × 7/39 × 7 = 56/273 and 9 × 13/21 × 13 = 117/273

Step 3: Add the Numerators
Now add the numerators (56 + 117 = 173) and keep the common denominator 273 unchanged.
Working: 56 + 117/273 = 173/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 173 and 273 is 1, confirming that 173/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 173/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 173 by denominator 273 produces a repeating decimal (approximately 0.6337, or 63.37%).
Working: 173 ÷ 273 = 0.6337 (63.37%)

Key Values:
- Simplified Fraction: 173/273
- Mixed Number Form: 173/273
- Decimal Value: 0.6337
- Percentage: 63.37%

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Solved with FractionsCalc:
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8/39 + 9/21 = 173/273

Simplified Fraction

173/273

Mixed Number

Proper (173/273)

Decimal Value

0.6337

Percentage

63.37%

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Step-by-Step Solution: 8/39 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 8/39 by 7, and multiply the numerator and denominator of 9/21 by 13 so both fractions share the common base 273.

8 × 7/39 × 7 = 56/273 and 9 × 13/21 × 13 = 117/273

Step 3

Add the Numerators

Now add the numerators (56 + 117 = 173) and keep the common denominator 273 unchanged.

56 + 117/273 = 173/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 173 and 273 is 1, confirming that 173/273 cannot be reduced further—it is already in its simplest irreducible form.

173/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 173 by denominator 273 produces a repeating decimal (approximately 0.6337, or 63.37%).

173 ÷ 273 = 0.6337 (63.37%)

Visual Representation

The diagram below illustrates 8/39 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`173/273`
Mixed Number Form	`173/273`
Decimal Form	`0.6337`
Percentage	`63.37%`

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Frequently Asked Questions

What is 8/39 plus 9/21 as a fraction?

8/39 + 9/21 in simplest fraction form is 173/273.

What is 8/39 plus 9/21 as a decimal?

8/39 + 9/21 converted to a decimal is 0.6337.

What is 8/39 plus 9/21 as a percentage?

8/39 + 9/21 expressed as a percentage is 63.37%.

Does 8/39 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.6337...) because the denominator contains prime factors other than 2 and 5.