What is 1/8 plus 5/9? (Answer: 49/72)

Exact Answer

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Problem: What is 1/8 plus 5/9?
Formula / Expression: 1/8 + 5/9
Final Answer: 49/72
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 1/8 by 9, and multiply the numerator and denominator of 5/9 by 8 so both fractions share the common base 72.
Working: 1 × 9/8 × 9 = 9/72 and 5 × 8/9 × 8 = 40/72

Step 3: Add the Numerators
Now add the numerators (9 + 40 = 49) and keep the common denominator 72 unchanged.
Working: 9 + 40/72 = 49/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 72 is 1, confirming that 49/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 72 produces a repeating decimal (approximately 0.680556, or 68.0556%).
Working: 49 ÷ 72 = 0.680556 (68.0556%)

Key Values:
- Simplified Fraction: 49/72
- Mixed Number Form: 49/72
- Decimal Value: 0.680556
- Percentage: 68.0556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-8-plus-5-9/
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1/8 + 5/9 = 49/72

Simplified Fraction

49/72

Mixed Number

Proper (49/72)

Decimal Value

0.680556

Percentage

68.0556%

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Step-by-Step Solution: 1/8 + 5/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 9) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 1/8 by 9, and multiply the numerator and denominator of 5/9 by 8 so both fractions share the common base 72.

1 × 9/8 × 9 = 9/72 and 5 × 8/9 × 8 = 40/72

Step 3

Add the Numerators

Now add the numerators (9 + 40 = 49) and keep the common denominator 72 unchanged.

9 + 40/72 = 49/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 72 is 1, confirming that 49/72 cannot be reduced further—it is already in its simplest irreducible form.

49/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 72 produces a repeating decimal (approximately 0.680556, or 68.0556%).

49 ÷ 72 = 0.680556 (68.0556%)

Visual Representation

The diagram below illustrates 1/8 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/72`
Mixed Number Form	`49/72`
Decimal Form	`0.680556`
Percentage	`68.0556%`

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Frequently Asked Questions

What is 1/8 plus 5/9 as a fraction?

1/8 + 5/9 in simplest fraction form is 49/72.

What is 1/8 plus 5/9 as a decimal?

1/8 + 5/9 converted to a decimal is 0.680556.

What is 1/8 plus 5/9 as a percentage?

1/8 + 5/9 expressed as a percentage is 68.0556%.

Does 1/8 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.680556...) because the denominator contains prime factors other than 2 and 5.