What is 3/21 plus 6/39? (Answer: 27/91)

Exact Answer

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Problem: What is 3/21 plus 6/39?
Formula / Expression: 3/21 + 6/39
Final Answer: 27/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 21 × 39 = 819, keeping the calculation simpler).
Working: LCD(21, 39) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 3/21 by 13, and multiply the numerator and denominator of 6/39 by 7 so both fractions share the common base 273.
Working: 3 × 13/21 × 13 = 39/273 and 6 × 7/39 × 7 = 42/273

Step 3: Add the Numerators
Now add the numerators (39 + 42 = 81) and keep the common denominator 273 unchanged.
Working: 39 + 42/273 = 81/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 81 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 81 ÷ 3/273 ÷ 3 = 27/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 91 produces a repeating decimal (approximately 0.296703, or 29.6703%).
Working: 27 ÷ 91 = 0.296703 (29.6703%)

Key Values:
- Simplified Fraction: 27/91
- Mixed Number Form: 27/91
- Decimal Value: 0.296703
- Percentage: 29.6703%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-6-39/
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3/21 + 6/39 = 27/91

Simplified Fraction

27/91

Mixed Number

Proper (27/91)

Decimal Value

0.296703

Percentage

29.6703%

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Step-by-Step Solution: 3/21 + 6/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 21 × 39 = 819, keeping the calculation simpler).

LCD(21, 39) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 3/21 by 13, and multiply the numerator and denominator of 6/39 by 7 so both fractions share the common base 273.

3 × 13/21 × 13 = 39/273 and 6 × 7/39 × 7 = 42/273

Step 3

Add the Numerators

Now add the numerators (39 + 42 = 81) and keep the common denominator 273 unchanged.

39 + 42/273 = 81/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 81 and 273, which is 3. Divide both the numerator and denominator by 3.

81 ÷ 3/273 ÷ 3 = 27/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 91 produces a repeating decimal (approximately 0.296703, or 29.6703%).

27 ÷ 91 = 0.296703 (29.6703%)

Visual Representation

The diagram below illustrates 3/21 plus 6/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/91`
Mixed Number Form	`27/91`
Decimal Form	`0.296703`
Percentage	`29.6703%`

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Frequently Asked Questions

What is 3/21 plus 6/39 as a fraction?

3/21 + 6/39 in simplest fraction form is 27/91.

What is 3/21 plus 6/39 as a decimal?

3/21 + 6/39 converted to a decimal is 0.296703.

What is 3/21 plus 6/39 as a percentage?

3/21 + 6/39 expressed as a percentage is 29.6703%.

Does 3/21 plus 6/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.296703...) because the denominator contains prime factors other than 2 and 5.