What is 2/7 plus 7/9? (Answer: 67/63)

Exact Answer

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Problem: What is 2/7 plus 7/9?
Formula / Expression: 2/7 + 7/9
Final Answer: 1 4/63 (67/63)
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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 7/9 by 7 so both fractions share the common base 63.
Working: 2 × 9/7 × 9 = 18/63 and 7 × 7/9 × 7 = 49/63

Step 3: Add the Numerators
Now add the numerators (18 + 49 = 67) and keep the common denominator 63 unchanged.
Working: 18 + 49/63 = 67/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 63 is 1, confirming that 67/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (67) is greater than the denominator (63), divide 67 by 63: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/63.
Working: 67/63 = 1 4/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 63 produces a repeating decimal (approximately 1.063492, or 106.3492%).
Working: 67 ÷ 63 = 1.063492 (106.3492%)

Key Values:
- Simplified Fraction: 67/63
- Mixed Number Form: 1 4/63
- Decimal Value: 1.063492
- Percentage: 106.3492%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-7-9/
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2/7 + 7/9 = 67/63

Simplified Fraction

67/63

Mixed Number

1 4/63

Decimal Value

1.063492

Percentage

106.3492%

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

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 7/9 by 7 so both fractions share the common base 63.

2 × 9/7 × 9 = 18/63 and 7 × 7/9 × 7 = 49/63

Step 3

Add the Numerators

Now add the numerators (18 + 49 = 67) and keep the common denominator 63 unchanged.

18 + 49/63 = 67/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 63 is 1, confirming that 67/63 cannot be reduced further—it is already in its simplest irreducible form.

67/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (67) is greater than the denominator (63), divide 67 by 63: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/63.

67/63 = 14/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 63 produces a repeating decimal (approximately 1.063492, or 106.3492%).

67 ÷ 63 = 1.063492 (106.3492%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/63`
Mixed Number Form	`1 4/63`
Decimal Form	`1.063492`
Percentage	`106.3492%`

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Frequently Asked Questions

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

2/7 + 7/9 in simplest fraction form is 67/63 (or 1 4/63 as a mixed number).

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

2/7 + 7/9 converted to a decimal is 1.063492.

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

2/7 + 7/9 expressed as a percentage is 106.3492%.

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

Because the numerator is greater than the denominator, the improper fraction 67/63 can be written as the mixed number 1 4/63.

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

It results in a repeating decimal (approximately 1.063492...) because the denominator contains prime factors other than 2 and 5.