What is 2/7 plus 5/9? (Answer: 53/63)

Exact Answer

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Problem: What is 2/7 plus 5/9?
Formula / Expression: 2/7 + 5/9
Final Answer: 53/63
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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 5/9 by 7 so both fractions share the common base 63.
Working: 2 × 9/7 × 9 = 18/63 and 5 × 7/9 × 7 = 35/63

Step 3: Add the Numerators
Now add the numerators (18 + 35 = 53) and keep the common denominator 63 unchanged.
Working: 18 + 35/63 = 53/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 63 is 1, confirming that 53/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 63 produces a repeating decimal (approximately 0.84127, or 84.127%).
Working: 53 ÷ 63 = 0.84127 (84.127%)

Key Values:
- Simplified Fraction: 53/63
- Mixed Number Form: 53/63
- Decimal Value: 0.84127
- Percentage: 84.127%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-5-9/
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2/7 + 5/9 = 53/63

Simplified Fraction

53/63

Mixed Number

Proper (53/63)

Decimal Value

0.84127

Percentage

84.127%

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Step-by-Step Solution: 2/7 + 5/9

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 5/9 by 7 so both fractions share the common base 63.

2 × 9/7 × 9 = 18/63 and 5 × 7/9 × 7 = 35/63

Step 3

Add the Numerators

Now add the numerators (18 + 35 = 53) and keep the common denominator 63 unchanged.

18 + 35/63 = 53/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 63 is 1, confirming that 53/63 cannot be reduced further—it is already in its simplest irreducible form.

53/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 63 produces a repeating decimal (approximately 0.84127, or 84.127%).

53 ÷ 63 = 0.84127 (84.127%)

Visual Representation

The diagram below illustrates 2/7 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/63`
Mixed Number Form	`53/63`
Decimal Form	`0.84127`
Percentage	`84.127%`

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Frequently Asked Questions

What is 2/7 plus 5/9 as a fraction?

2/7 + 5/9 in simplest fraction form is 53/63.

What is 2/7 plus 5/9 as a decimal?

2/7 + 5/9 converted to a decimal is 0.84127.

What is 2/7 plus 5/9 as a percentage?

2/7 + 5/9 expressed as a percentage is 84.127%.

Does 2/7 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.84127...) because the denominator contains prime factors other than 2 and 5.