What is 3/7 plus 2/3? (Answer: 23/21)

Exact Answer

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Problem: What is 3/7 plus 2/3?
Formula / Expression: 3/7 + 2/3
Final Answer: 1 2/21 (23/21)
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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 3/7 by 3, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.
Working: 3 × 3/7 × 3 = 9/21 and 2 × 7/3 × 7 = 14/21

Step 3: Add the Numerators
Now add the numerators (9 + 14 = 23) and keep the common denominator 21 unchanged.
Working: 9 + 14/21 = 23/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 21 is 1, confirming that 23/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/21

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (23) is greater than the denominator (21), divide 23 by 21: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/21.
Working: 23/21 = 1 2/21

Step 6: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 21 produces a repeating decimal (approximately 1.095238, or 109.5238%).
Working: 23 ÷ 21 = 1.095238 (109.5238%)

Key Values:
- Simplified Fraction: 23/21
- Mixed Number Form: 1 2/21
- Decimal Value: 1.095238
- Percentage: 109.5238%

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Solved with FractionsCalc:
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3/7 + 2/3 = 23/21

Simplified Fraction

23/21

Mixed Number

1 2/21

Decimal Value

1.095238

Percentage

109.5238%

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Step-by-Step Solution: 3/7 + 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 3/7 by 3, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.

3 × 3/7 × 3 = 9/21 and 2 × 7/3 × 7 = 14/21

Step 3

Add the Numerators

Now add the numerators (9 + 14 = 23) and keep the common denominator 21 unchanged.

9 + 14/21 = 23/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 21 is 1, confirming that 23/21 cannot be reduced further—it is already in its simplest irreducible form.

23/21

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (23) is greater than the denominator (21), divide 23 by 21: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/21.

23/21 = 12/21

Step 6

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 21 produces a repeating decimal (approximately 1.095238, or 109.5238%).

23 ÷ 21 = 1.095238 (109.5238%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/21`
Mixed Number Form	`1 2/21`
Decimal Form	`1.095238`
Percentage	`109.5238%`

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Frequently Asked Questions

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

3/7 + 2/3 in simplest fraction form is 23/21 (or 1 2/21 as a mixed number).

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

3/7 + 2/3 converted to a decimal is 1.095238.

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

3/7 + 2/3 expressed as a percentage is 109.5238%.

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

Because the numerator is greater than the denominator, the improper fraction 23/21 can be written as the mixed number 1 2/21.

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

It results in a repeating decimal (approximately 1.095238...) because the denominator contains prime factors other than 2 and 5.