What is 8/39 plus 5/21? (Answer: 121/273)

Exact Answer

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Problem: What is 8/39 plus 5/21?
Formula / Expression: 8/39 + 5/21
Final Answer: 121/273
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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 5/21 by 13 so both fractions share the common base 273.
Working: 8 × 7/39 × 7 = 56/273 and 5 × 13/21 × 13 = 65/273

Step 3: Add the Numerators
Now add the numerators (56 + 65 = 121) and keep the common denominator 273 unchanged.
Working: 56 + 65/273 = 121/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 121 and 273 is 1, confirming that 121/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 121/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 121 by denominator 273 produces a repeating decimal (approximately 0.443223, or 44.3223%).
Working: 121 ÷ 273 = 0.443223 (44.3223%)

Key Values:
- Simplified Fraction: 121/273
- Mixed Number Form: 121/273
- Decimal Value: 0.443223
- Percentage: 44.3223%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-39-plus-5-21/
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8/39 + 5/21 = 121/273

Simplified Fraction

121/273

Mixed Number

Proper (121/273)

Decimal Value

0.443223

Percentage

44.3223%

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Step-by-Step Solution: 8/39 + 5/21

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 5/21 by 13 so both fractions share the common base 273.

8 × 7/39 × 7 = 56/273 and 5 × 13/21 × 13 = 65/273

Step 3

Add the Numerators

Now add the numerators (56 + 65 = 121) and keep the common denominator 273 unchanged.

56 + 65/273 = 121/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 121 and 273 is 1, confirming that 121/273 cannot be reduced further—it is already in its simplest irreducible form.

121/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 121 by denominator 273 produces a repeating decimal (approximately 0.443223, or 44.3223%).

121 ÷ 273 = 0.443223 (44.3223%)

Visual Representation

The diagram below illustrates 8/39 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`121/273`
Mixed Number Form	`121/273`
Decimal Form	`0.443223`
Percentage	`44.3223%`

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Frequently Asked Questions

What is 8/39 plus 5/21 as a fraction?

8/39 + 5/21 in simplest fraction form is 121/273.

What is 8/39 plus 5/21 as a decimal?

8/39 + 5/21 converted to a decimal is 0.443223.

What is 8/39 plus 5/21 as a percentage?

8/39 + 5/21 expressed as a percentage is 44.3223%.

Does 8/39 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.443223...) because the denominator contains prime factors other than 2 and 5.