What is 2/7 plus 1/3? (Answer: 13/21)

Exact Answer

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Problem: What is 2/7 plus 1/3?
Formula / Expression: 2/7 + 1/3
Final Answer: 13/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 3 = 21.
Working: LCD(7, 3) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 2/7 by 3, and multiply the numerator and denominator of 1/3 by 7 so both fractions share the common base 21.
Working: 2 × 3/7 × 3 = 6/21 and 1 × 7/3 × 7 = 7/21

Step 3: Add the Numerators
Now add the numerators (6 + 7 = 13) and keep the common denominator 21 unchanged.
Working: 6 + 7/21 = 13/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 21 is 1, confirming that 13/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).
Working: 13 ÷ 21 = 0.619048 (61.9048%)

Key Values:
- Simplified Fraction: 13/21
- Mixed Number Form: 13/21
- Decimal Value: 0.619048
- Percentage: 61.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-1-3/
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2/7 + 1/3 = 13/21

Simplified Fraction

13/21

Mixed Number

Proper (13/21)

Decimal Value

0.619048

Percentage

61.9048%

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Step-by-Step Solution: 2/7 + 1/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 3 = 21.

LCD(7, 3) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 2/7 by 3, and multiply the numerator and denominator of 1/3 by 7 so both fractions share the common base 21.

2 × 3/7 × 3 = 6/21 and 1 × 7/3 × 7 = 7/21

Step 3

Add the Numerators

Now add the numerators (6 + 7 = 13) and keep the common denominator 21 unchanged.

6 + 7/21 = 13/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 21 is 1, confirming that 13/21 cannot be reduced further—it is already in its simplest irreducible form.

13/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).

13 ÷ 21 = 0.619048 (61.9048%)

Visual Representation

The diagram below illustrates 2/7 plus 1/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/21`
Mixed Number Form	`13/21`
Decimal Form	`0.619048`
Percentage	`61.9048%`

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Frequently Asked Questions

What is 2/7 plus 1/3 as a fraction?

2/7 + 1/3 in simplest fraction form is 13/21.

What is 2/7 plus 1/3 as a decimal?

2/7 + 1/3 converted to a decimal is 0.619048.

What is 2/7 plus 1/3 as a percentage?

2/7 + 1/3 expressed as a percentage is 61.9048%.

Does 2/7 plus 1/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.619048...) because the denominator contains prime factors other than 2 and 5.