What is 2/9 plus 5/7? (Answer: 59/63)

Exact Answer

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Problem: What is 2/9 plus 5/7?
Formula / Expression: 2/9 + 5/7
Final Answer: 59/63
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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 5/7 by 9 so both fractions share the common base 63.
Working: 2 × 7/9 × 7 = 14/63 and 5 × 9/7 × 9 = 45/63

Step 3: Add the Numerators
Now add the numerators (14 + 45 = 59) and keep the common denominator 63 unchanged.
Working: 14 + 45/63 = 59/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 63 is 1, confirming that 59/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 63 produces a repeating decimal (approximately 0.936508, or 93.6508%).
Working: 59 ÷ 63 = 0.936508 (93.6508%)

Key Values:
- Simplified Fraction: 59/63
- Mixed Number Form: 59/63
- Decimal Value: 0.936508
- Percentage: 93.6508%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-5-7/
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2/9 + 5/7 = 59/63

Simplified Fraction

59/63

Mixed Number

Proper (59/63)

Decimal Value

0.936508

Percentage

93.6508%

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

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

2 × 7/9 × 7 = 14/63 and 5 × 9/7 × 9 = 45/63

Step 3

Add the Numerators

Now add the numerators (14 + 45 = 59) and keep the common denominator 63 unchanged.

14 + 45/63 = 59/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 63 is 1, confirming that 59/63 cannot be reduced further—it is already in its simplest irreducible form.

59/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 63 produces a repeating decimal (approximately 0.936508, or 93.6508%).

59 ÷ 63 = 0.936508 (93.6508%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/63`
Mixed Number Form	`59/63`
Decimal Form	`0.936508`
Percentage	`93.6508%`

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Frequently Asked Questions

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

2/9 + 5/7 in simplest fraction form is 59/63.

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

2/9 + 5/7 converted to a decimal is 0.936508.

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

2/9 + 5/7 expressed as a percentage is 93.6508%.

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

It results in a repeating decimal (approximately 0.936508...) because the denominator contains prime factors other than 2 and 5.