What is 9/24 plus 5/9? (Answer: 67/72)

Exact Answer

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Problem: What is 9/24 plus 5/9?
Formula / Expression: 9/24 + 5/9
Final Answer: 67/72
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 24 × 9 = 216, keeping the calculation simpler).
Working: LCD(24, 9) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 9/24 by 3, and multiply the numerator and denominator of 5/9 by 8 so both fractions share the common base 72.
Working: 9 × 3/24 × 3 = 27/72 and 5 × 8/9 × 8 = 40/72

Step 3: Add the Numerators
Now add the numerators (27 + 40 = 67) and keep the common denominator 72 unchanged.
Working: 27 + 40/72 = 67/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 72 is 1, confirming that 67/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 72 produces a repeating decimal (approximately 0.930556, or 93.0556%).
Working: 67 ÷ 72 = 0.930556 (93.0556%)

Key Values:
- Simplified Fraction: 67/72
- Mixed Number Form: 67/72
- Decimal Value: 0.930556
- Percentage: 93.0556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-24-plus-5-9/
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9/24 + 5/9 = 67/72

Simplified Fraction

67/72

Mixed Number

Proper (67/72)

Decimal Value

0.930556

Percentage

93.0556%

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Step-by-Step Solution: 9/24 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 24 × 9 = 216, keeping the calculation simpler).

LCD(24, 9) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 9/24 by 3, and multiply the numerator and denominator of 5/9 by 8 so both fractions share the common base 72.

9 × 3/24 × 3 = 27/72 and 5 × 8/9 × 8 = 40/72

Step 3

Add the Numerators

Now add the numerators (27 + 40 = 67) and keep the common denominator 72 unchanged.

27 + 40/72 = 67/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 72 is 1, confirming that 67/72 cannot be reduced further—it is already in its simplest irreducible form.

67/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 72 produces a repeating decimal (approximately 0.930556, or 93.0556%).

67 ÷ 72 = 0.930556 (93.0556%)

Visual Representation

The diagram below illustrates 9/24 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/72`
Mixed Number Form	`67/72`
Decimal Form	`0.930556`
Percentage	`93.0556%`

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Frequently Asked Questions

What is 9/24 plus 5/9 as a fraction?

9/24 + 5/9 in simplest fraction form is 67/72.

What is 9/24 plus 5/9 as a decimal?

9/24 + 5/9 converted to a decimal is 0.930556.

What is 9/24 plus 5/9 as a percentage?

9/24 + 5/9 expressed as a percentage is 93.0556%.

Does 9/24 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.930556...) because the denominator contains prime factors other than 2 and 5.