What is 1/7 plus 2/3? (Answer: 17/21)

Exact Answer

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Problem: What is 1/7 plus 2/3?
Formula / Expression: 1/7 + 2/3
Final Answer: 17/21
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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 1/7 by 3, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.
Working: 1 × 3/7 × 3 = 3/21 and 2 × 7/3 × 7 = 14/21

Step 3: Add the Numerators
Now add the numerators (3 + 14 = 17) and keep the common denominator 21 unchanged.
Working: 3 + 14/21 = 17/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 21 is 1, confirming that 17/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).
Working: 17 ÷ 21 = 0.809524 (80.9524%)

Key Values:
- Simplified Fraction: 17/21
- Mixed Number Form: 17/21
- Decimal Value: 0.809524
- Percentage: 80.9524%

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Solved with FractionsCalc:
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1/7 + 2/3 = 17/21

Simplified Fraction

17/21

Mixed Number

Proper (17/21)

Decimal Value

0.809524

Percentage

80.9524%

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

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

1 × 3/7 × 3 = 3/21 and 2 × 7/3 × 7 = 14/21

Step 3

Add the Numerators

Now add the numerators (3 + 14 = 17) and keep the common denominator 21 unchanged.

3 + 14/21 = 17/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 21 is 1, confirming that 17/21 cannot be reduced further—it is already in its simplest irreducible form.

17/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).

17 ÷ 21 = 0.809524 (80.9524%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/21`
Mixed Number Form	`17/21`
Decimal Form	`0.809524`
Percentage	`80.9524%`

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Frequently Asked Questions

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

1/7 + 2/3 in simplest fraction form is 17/21.

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

1/7 + 2/3 converted to a decimal is 0.809524.

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

1/7 + 2/3 expressed as a percentage is 80.9524%.

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

It results in a repeating decimal (approximately 0.809524...) because the denominator contains prime factors other than 2 and 5.