What is 2/7 plus 6/9? (Answer: 20/21)

Exact Answer

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Problem: What is 2/7 plus 6/9?
Formula / Expression: 2/7 + 6/9
Final Answer: 20/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.
Working: LCD(7, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 2/7 by 9, and multiply the numerator and denominator of 6/9 by 7 so both fractions share the common base 63.
Working: 2 × 9/7 × 9 = 18/63 and 6 × 7/9 × 7 = 42/63

Step 3: Add the Numerators
Now add the numerators (18 + 42 = 60) and keep the common denominator 63 unchanged.
Working: 18 + 42/63 = 60/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 60 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: 60 ÷ 3/63 ÷ 3 = 20/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 21 produces a repeating decimal (approximately 0.952381, or 95.2381%).
Working: 20 ÷ 21 = 0.952381 (95.2381%)

Key Values:
- Simplified Fraction: 20/21
- Mixed Number Form: 20/21
- Decimal Value: 0.952381
- Percentage: 95.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-6-9/
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2/7 + 6/9 = 20/21

Simplified Fraction

20/21

Mixed Number

Proper (20/21)

Decimal Value

0.952381

Percentage

95.2381%

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Step-by-Step Solution: 2/7 + 6/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.

LCD(7, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 2/7 by 9, and multiply the numerator and denominator of 6/9 by 7 so both fractions share the common base 63.

2 × 9/7 × 9 = 18/63 and 6 × 7/9 × 7 = 42/63

Step 3

Add the Numerators

Now add the numerators (18 + 42 = 60) and keep the common denominator 63 unchanged.

18 + 42/63 = 60/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 60 and 63, which is 3. Divide both the numerator and denominator by 3.

60 ÷ 3/63 ÷ 3 = 20/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 21 produces a repeating decimal (approximately 0.952381, or 95.2381%).

20 ÷ 21 = 0.952381 (95.2381%)

Visual Representation

The diagram below illustrates 2/7 plus 6/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/21`
Mixed Number Form	`20/21`
Decimal Form	`0.952381`
Percentage	`95.2381%`

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Frequently Asked Questions

What is 2/7 plus 6/9 as a fraction?

2/7 + 6/9 in simplest fraction form is 20/21.

What is 2/7 plus 6/9 as a decimal?

2/7 + 6/9 converted to a decimal is 0.952381.

What is 2/7 plus 6/9 as a percentage?

2/7 + 6/9 expressed as a percentage is 95.2381%.

Does 2/7 plus 6/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.952381...) because the denominator contains prime factors other than 2 and 5.