What is 8/39 plus 8/21? (Answer: 160/273)

Exact Answer

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Problem: What is 8/39 plus 8/21?
Formula / Expression: 8/39 + 8/21
Final Answer: 160/273
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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 8/21 by 13 so both fractions share the common base 273.
Working: 8 × 7/39 × 7 = 56/273 and 8 × 13/21 × 13 = 104/273

Step 3: Add the Numerators
Now add the numerators (56 + 104 = 160) and keep the common denominator 273 unchanged.
Working: 56 + 104/273 = 160/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 160 and 273 is 1, confirming that 160/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 160/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 160 by denominator 273 produces a repeating decimal (approximately 0.586081, or 58.6081%).
Working: 160 ÷ 273 = 0.586081 (58.6081%)

Key Values:
- Simplified Fraction: 160/273
- Mixed Number Form: 160/273
- Decimal Value: 0.586081
- Percentage: 58.6081%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-39-plus-8-21/
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8/39 + 8/21 = 160/273

Simplified Fraction

160/273

Mixed Number

Proper (160/273)

Decimal Value

0.586081

Percentage

58.6081%

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Step-by-Step Solution: 8/39 + 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 8/39 by 7, and multiply the numerator and denominator of 8/21 by 13 so both fractions share the common base 273.

8 × 7/39 × 7 = 56/273 and 8 × 13/21 × 13 = 104/273

Step 3

Add the Numerators

Now add the numerators (56 + 104 = 160) and keep the common denominator 273 unchanged.

56 + 104/273 = 160/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 160 and 273 is 1, confirming that 160/273 cannot be reduced further—it is already in its simplest irreducible form.

160/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 160 by denominator 273 produces a repeating decimal (approximately 0.586081, or 58.6081%).

160 ÷ 273 = 0.586081 (58.6081%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`160/273`
Mixed Number Form	`160/273`
Decimal Form	`0.586081`
Percentage	`58.6081%`

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Frequently Asked Questions

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

8/39 + 8/21 in simplest fraction form is 160/273.

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

8/39 + 8/21 converted to a decimal is 0.586081.

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

8/39 + 8/21 expressed as a percentage is 58.6081%.

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

It results in a repeating decimal (approximately 0.586081...) because the denominator contains prime factors other than 2 and 5.