What is 13/39 plus 11/21? (Answer: 6/7)

Exact Answer

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Problem: What is 13/39 plus 11/21?
Formula / Expression: 13/39 + 11/21
Final Answer: 6/7
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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 13/39 by 7, and multiply the numerator and denominator of 11/21 by 13 so both fractions share the common base 273.
Working: 13 × 7/39 × 7 = 91/273 and 11 × 13/21 × 13 = 143/273

Step 3: Add the Numerators
Now add the numerators (91 + 143 = 234) and keep the common denominator 273 unchanged.
Working: 91 + 143/273 = 234/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 234 and 273, which is 39. Divide both the numerator and denominator by 39.
Working: 234 ÷ 39/273 ÷ 39 = 6/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).
Working: 6 ÷ 7 = 0.857143 (85.7143%)

Key Values:
- Simplified Fraction: 6/7
- Mixed Number Form: 6/7
- Decimal Value: 0.857143
- Percentage: 85.7143%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-39-plus-11-21/
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13/39 + 11/21 = 6/7

Simplified Fraction

6/7

Mixed Number

Proper (6/7)

Decimal Value

0.857143

Percentage

85.7143%

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Step-by-Step Solution: 13/39 + 11/21

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 13/39 by 7, and multiply the numerator and denominator of 11/21 by 13 so both fractions share the common base 273.

13 × 7/39 × 7 = 91/273 and 11 × 13/21 × 13 = 143/273

Step 3

Add the Numerators

Now add the numerators (91 + 143 = 234) and keep the common denominator 273 unchanged.

91 + 143/273 = 234/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 234 and 273, which is 39. Divide both the numerator and denominator by 39.

234 ÷ 39/273 ÷ 39 = 6/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).

6 ÷ 7 = 0.857143 (85.7143%)

Visual Representation

The diagram below illustrates 13/39 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/7`
Mixed Number Form	`6/7`
Decimal Form	`0.857143`
Percentage	`85.7143%`

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Frequently Asked Questions

What is 13/39 plus 11/21 as a fraction?

13/39 + 11/21 in simplest fraction form is 6/7.

What is 13/39 plus 11/21 as a decimal?

13/39 + 11/21 converted to a decimal is 0.857143.

What is 13/39 plus 11/21 as a percentage?

13/39 + 11/21 expressed as a percentage is 85.7143%.

Does 13/39 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.857143...) because the denominator contains prime factors other than 2 and 5.