What is 2/9 plus 6/7? (Answer: 68/63)

Exact Answer

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Problem: What is 2/9 plus 6/7?
Formula / Expression: 2/9 + 6/7
Final Answer: 1 5/63 (68/63)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 2/9 by 7, and multiply the numerator and denominator of 6/7 by 9 so both fractions share the common base 63.
Working: 2 × 7/9 × 7 = 14/63 and 6 × 9/7 × 9 = 54/63

Step 3: Add the Numerators
Now add the numerators (14 + 54 = 68) and keep the common denominator 63 unchanged.
Working: 14 + 54/63 = 68/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 68 and 63 is 1, confirming that 68/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 68/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (68) is greater than the denominator (63), divide 68 by 63: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/63.
Working: 68/63 = 1 5/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 68 by denominator 63 produces a repeating decimal (approximately 1.079365, or 107.9365%).
Working: 68 ÷ 63 = 1.079365 (107.9365%)

Key Values:
- Simplified Fraction: 68/63
- Mixed Number Form: 1 5/63
- Decimal Value: 1.079365
- Percentage: 107.9365%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-6-7/
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2/9 + 6/7 = 68/63

Simplified Fraction

68/63

Mixed Number

1 5/63

Decimal Value

1.079365

Percentage

107.9365%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 7) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

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

2 × 7/9 × 7 = 14/63 and 6 × 9/7 × 9 = 54/63

Step 3

Add the Numerators

Now add the numerators (14 + 54 = 68) and keep the common denominator 63 unchanged.

14 + 54/63 = 68/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 68 and 63 is 1, confirming that 68/63 cannot be reduced further—it is already in its simplest irreducible form.

68/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (68) is greater than the denominator (63), divide 68 by 63: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/63.

68/63 = 15/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 68 by denominator 63 produces a repeating decimal (approximately 1.079365, or 107.9365%).

68 ÷ 63 = 1.079365 (107.9365%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`68/63`
Mixed Number Form	`1 5/63`
Decimal Form	`1.079365`
Percentage	`107.9365%`

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Frequently Asked Questions

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

2/9 + 6/7 in simplest fraction form is 68/63 (or 1 5/63 as a mixed number).

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

2/9 + 6/7 converted to a decimal is 1.079365.

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

2/9 + 6/7 expressed as a percentage is 107.9365%.

How do you write 2/9 plus 6/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 68/63 can be written as the mixed number 1 5/63.

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

It results in a repeating decimal (approximately 1.079365...) because the denominator contains prime factors other than 2 and 5.