What is 8/39 plus 12/21? (Answer: 212/273)

Exact Answer

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Problem: What is 8/39 plus 12/21?
Formula / Expression: 8/39 + 12/21
Final Answer: 212/273
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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 12/21 by 13 so both fractions share the common base 273.
Working: 8 × 7/39 × 7 = 56/273 and 12 × 13/21 × 13 = 156/273

Step 3: Add the Numerators
Now add the numerators (56 + 156 = 212) and keep the common denominator 273 unchanged.
Working: 56 + 156/273 = 212/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 212 and 273 is 1, confirming that 212/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 212/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 212 by denominator 273 produces a repeating decimal (approximately 0.776557, or 77.6557%).
Working: 212 ÷ 273 = 0.776557 (77.6557%)

Key Values:
- Simplified Fraction: 212/273
- Mixed Number Form: 212/273
- Decimal Value: 0.776557
- Percentage: 77.6557%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-39-plus-12-21/
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8/39 + 12/21 = 212/273

Simplified Fraction

212/273

Mixed Number

Proper (212/273)

Decimal Value

0.776557

Percentage

77.6557%

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Step-by-Step Solution: 8/39 + 12/21

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 12/21 by 13 so both fractions share the common base 273.

8 × 7/39 × 7 = 56/273 and 12 × 13/21 × 13 = 156/273

Step 3

Add the Numerators

Now add the numerators (56 + 156 = 212) and keep the common denominator 273 unchanged.

56 + 156/273 = 212/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 212 and 273 is 1, confirming that 212/273 cannot be reduced further—it is already in its simplest irreducible form.

212/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 212 by denominator 273 produces a repeating decimal (approximately 0.776557, or 77.6557%).

212 ÷ 273 = 0.776557 (77.6557%)

Visual Representation

The diagram below illustrates 8/39 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`212/273`
Mixed Number Form	`212/273`
Decimal Form	`0.776557`
Percentage	`77.6557%`

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Frequently Asked Questions

What is 8/39 plus 12/21 as a fraction?

8/39 + 12/21 in simplest fraction form is 212/273.

What is 8/39 plus 12/21 as a decimal?

8/39 + 12/21 converted to a decimal is 0.776557.

What is 8/39 plus 12/21 as a percentage?

8/39 + 12/21 expressed as a percentage is 77.6557%.

Does 8/39 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.776557...) because the denominator contains prime factors other than 2 and 5.