What is 2/9 plus 5/8? (Answer: 61/72)

Exact Answer

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Problem: What is 2/9 plus 5/8?
Formula / Expression: 2/9 + 5/8
Final Answer: 61/72
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 8 = 72.
Working: LCD(9, 8) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 2/9 by 8, and multiply the numerator and denominator of 5/8 by 9 so both fractions share the common base 72.
Working: 2 × 8/9 × 8 = 16/72 and 5 × 9/8 × 9 = 45/72

Step 3: Add the Numerators
Now add the numerators (16 + 45 = 61) and keep the common denominator 72 unchanged.
Working: 16 + 45/72 = 61/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 72 is 1, confirming that 61/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 72 produces a repeating decimal (approximately 0.847222, or 84.7222%).
Working: 61 ÷ 72 = 0.847222 (84.7222%)

Key Values:
- Simplified Fraction: 61/72
- Mixed Number Form: 61/72
- Decimal Value: 0.847222
- Percentage: 84.7222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-5-8/
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2/9 + 5/8 = 61/72

Simplified Fraction

61/72

Mixed Number

Proper (61/72)

Decimal Value

0.847222

Percentage

84.7222%

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Step-by-Step Solution: 2/9 + 5/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 8 = 72.

LCD(9, 8) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 2/9 by 8, and multiply the numerator and denominator of 5/8 by 9 so both fractions share the common base 72.

2 × 8/9 × 8 = 16/72 and 5 × 9/8 × 9 = 45/72

Step 3

Add the Numerators

Now add the numerators (16 + 45 = 61) and keep the common denominator 72 unchanged.

16 + 45/72 = 61/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 72 is 1, confirming that 61/72 cannot be reduced further—it is already in its simplest irreducible form.

61/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 72 produces a repeating decimal (approximately 0.847222, or 84.7222%).

61 ÷ 72 = 0.847222 (84.7222%)

Visual Representation

The diagram below illustrates 2/9 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/72`
Mixed Number Form	`61/72`
Decimal Form	`0.847222`
Percentage	`84.7222%`

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Frequently Asked Questions

What is 2/9 plus 5/8 as a fraction?

2/9 + 5/8 in simplest fraction form is 61/72.

What is 2/9 plus 5/8 as a decimal?

2/9 + 5/8 converted to a decimal is 0.847222.

What is 2/9 plus 5/8 as a percentage?

2/9 + 5/8 expressed as a percentage is 84.7222%.

Does 2/9 plus 5/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.847222...) because the denominator contains prime factors other than 2 and 5.