What is 7/21 plus 13/39? (Answer: 2/3)

Exact Answer

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Problem: What is 7/21 plus 13/39?
Formula / Expression: 7/21 + 13/39
Final Answer: 2/3
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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 7/21 by 13, and multiply the numerator and denominator of 13/39 by 7 so both fractions share the common base 273.
Working: 7 × 13/21 × 13 = 91/273 and 13 × 7/39 × 7 = 91/273

Step 3: Add the Numerators
Now add the numerators (91 + 91 = 182) and keep the common denominator 273 unchanged.
Working: 91 + 91/273 = 182/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 182 and 273, which is 91. Divide both the numerator and denominator by 91.
Working: 182 ÷ 91/273 ÷ 91 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-21-plus-13-39/
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7/21 + 13/39 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 7/21 + 13/39

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

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

Step 3

Add the Numerators

Now add the numerators (91 + 91 = 182) and keep the common denominator 273 unchanged.

91 + 91/273 = 182/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 182 and 273, which is 91. Divide both the numerator and denominator by 91.

182 ÷ 91/273 ÷ 91 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 7/21 plus 13/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 7/21 plus 13/39 as a fraction?

7/21 + 13/39 in simplest fraction form is 2/3.

What is 7/21 plus 13/39 as a decimal?

7/21 + 13/39 converted to a decimal is 0.666667.

What is 7/21 plus 13/39 as a percentage?

7/21 + 13/39 expressed as a percentage is 66.6667%.

Does 7/21 plus 13/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.