What is 3/39 plus 8/21? (Answer: 125/273)

Exact Answer

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Problem: What is 3/39 plus 8/21?
Formula / Expression: 3/39 + 8/21
Final Answer: 125/273
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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 3/39 by 7, and multiply the numerator and denominator of 8/21 by 13 so both fractions share the common base 273.
Working: 3 × 7/39 × 7 = 21/273 and 8 × 13/21 × 13 = 104/273

Step 3: Add the Numerators
Now add the numerators (21 + 104 = 125) and keep the common denominator 273 unchanged.
Working: 21 + 104/273 = 125/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 125 and 273 is 1, confirming that 125/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 125/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 125 by denominator 273 produces a repeating decimal (approximately 0.457875, or 45.7875%).
Working: 125 ÷ 273 = 0.457875 (45.7875%)

Key Values:
- Simplified Fraction: 125/273
- Mixed Number Form: 125/273
- Decimal Value: 0.457875
- Percentage: 45.7875%

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Solved with FractionsCalc:
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3/39 + 8/21 = 125/273

Simplified Fraction

125/273

Mixed Number

Proper (125/273)

Decimal Value

0.457875

Percentage

45.7875%

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Step-by-Step Solution: 3/39 + 8/21

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 3/39 by 7, and multiply the numerator and denominator of 8/21 by 13 so both fractions share the common base 273.

3 × 7/39 × 7 = 21/273 and 8 × 13/21 × 13 = 104/273

Step 3

Add the Numerators

Now add the numerators (21 + 104 = 125) and keep the common denominator 273 unchanged.

21 + 104/273 = 125/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 125 and 273 is 1, confirming that 125/273 cannot be reduced further—it is already in its simplest irreducible form.

125/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 125 by denominator 273 produces a repeating decimal (approximately 0.457875, or 45.7875%).

125 ÷ 273 = 0.457875 (45.7875%)

Visual Representation

The diagram below illustrates 3/39 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`125/273`
Mixed Number Form	`125/273`
Decimal Form	`0.457875`
Percentage	`45.7875%`

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Frequently Asked Questions

What is 3/39 plus 8/21 as a fraction?

3/39 + 8/21 in simplest fraction form is 125/273.

What is 3/39 plus 8/21 as a decimal?

3/39 + 8/21 converted to a decimal is 0.457875.

What is 3/39 plus 8/21 as a percentage?

3/39 + 8/21 expressed as a percentage is 45.7875%.

Does 3/39 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.457875...) because the denominator contains prime factors other than 2 and 5.