What is 6/39 plus 6/21? (Answer: 40/91)

Exact Answer

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Problem: What is 6/39 plus 6/21?
Formula / Expression: 6/39 + 6/21
Final Answer: 40/91
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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 6/39 by 7, and multiply the numerator and denominator of 6/21 by 13 so both fractions share the common base 273.
Working: 6 × 7/39 × 7 = 42/273 and 6 × 13/21 × 13 = 78/273

Step 3: Add the Numerators
Now add the numerators (42 + 78 = 120) and keep the common denominator 273 unchanged.
Working: 42 + 78/273 = 120/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 120 ÷ 3/273 ÷ 3 = 40/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 91 produces a repeating decimal (approximately 0.43956, or 43.956%).
Working: 40 ÷ 91 = 0.43956 (43.956%)

Key Values:
- Simplified Fraction: 40/91
- Mixed Number Form: 40/91
- Decimal Value: 0.43956
- Percentage: 43.956%

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Solved with FractionsCalc:
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6/39 + 6/21 = 40/91

Simplified Fraction

40/91

Mixed Number

Proper (40/91)

Decimal Value

0.43956

Percentage

43.956%

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Step-by-Step Solution: 6/39 + 6/21

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 6/39 by 7, and multiply the numerator and denominator of 6/21 by 13 so both fractions share the common base 273.

6 × 7/39 × 7 = 42/273 and 6 × 13/21 × 13 = 78/273

Step 3

Add the Numerators

Now add the numerators (42 + 78 = 120) and keep the common denominator 273 unchanged.

42 + 78/273 = 120/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 273, which is 3. Divide both the numerator and denominator by 3.

120 ÷ 3/273 ÷ 3 = 40/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 91 produces a repeating decimal (approximately 0.43956, or 43.956%).

40 ÷ 91 = 0.43956 (43.956%)

Visual Representation

The diagram below illustrates 6/39 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/91`
Mixed Number Form	`40/91`
Decimal Form	`0.43956`
Percentage	`43.956%`

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Frequently Asked Questions

What is 6/39 plus 6/21 as a fraction?

6/39 + 6/21 in simplest fraction form is 40/91.

What is 6/39 plus 6/21 as a decimal?

6/39 + 6/21 converted to a decimal is 0.43956.

What is 6/39 plus 6/21 as a percentage?

6/39 + 6/21 expressed as a percentage is 43.956%.

Does 6/39 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.43956...) because the denominator contains prime factors other than 2 and 5.