What is 2/3 plus 6/7? (Answer: 32/21)

Exact Answer

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Problem: What is 2/3 plus 6/7?
Formula / Expression: 2/3 + 6/7
Final Answer: 1 11/21 (32/21)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 2/3 by 7, and multiply the numerator and denominator of 6/7 by 3 so both fractions share the common base 21.
Working: 2 × 7/3 × 7 = 14/21 and 6 × 3/7 × 3 = 18/21

Step 3: Add the Numerators
Now add the numerators (14 + 18 = 32) and keep the common denominator 21 unchanged.
Working: 14 + 18/21 = 32/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 32 and 21 is 1, confirming that 32/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 32/21

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (32) is greater than the denominator (21), divide 32 by 21: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/21.
Working: 32/21 = 1 11/21

Step 6: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 21 produces a repeating decimal (approximately 1.52381, or 152.381%).
Working: 32 ÷ 21 = 1.52381 (152.381%)

Key Values:
- Simplified Fraction: 32/21
- Mixed Number Form: 1 11/21
- Decimal Value: 1.52381
- Percentage: 152.381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-3-plus-6-7/
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2/3 + 6/7 = 32/21

Simplified Fraction

32/21

Mixed Number

1 11/21

Decimal Value

1.52381

Percentage

152.381%

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Step-by-Step Solution: 2/3 + 6/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(3, 7) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 2/3 by 7, and multiply the numerator and denominator of 6/7 by 3 so both fractions share the common base 21.

2 × 7/3 × 7 = 14/21 and 6 × 3/7 × 3 = 18/21

Step 3

Add the Numerators

Now add the numerators (14 + 18 = 32) and keep the common denominator 21 unchanged.

14 + 18/21 = 32/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 32 and 21 is 1, confirming that 32/21 cannot be reduced further—it is already in its simplest irreducible form.

32/21

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (32) is greater than the denominator (21), divide 32 by 21: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/21.

32/21 = 111/21

Step 6

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 21 produces a repeating decimal (approximately 1.52381, or 152.381%).

32 ÷ 21 = 1.52381 (152.381%)

Visual Representation

The diagram below illustrates 2/3 plus 6/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/21`
Mixed Number Form	`1 11/21`
Decimal Form	`1.52381`
Percentage	`152.381%`

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Frequently Asked Questions

What is 2/3 plus 6/7 as a fraction?

2/3 + 6/7 in simplest fraction form is 32/21 (or 1 11/21 as a mixed number).

What is 2/3 plus 6/7 as a decimal?

2/3 + 6/7 converted to a decimal is 1.52381.

What is 2/3 plus 6/7 as a percentage?

2/3 + 6/7 expressed as a percentage is 152.381%.

How do you write 2/3 plus 6/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 32/21 can be written as the mixed number 1 11/21.

Does 2/3 plus 6/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.52381...) because the denominator contains prime factors other than 2 and 5.