What is 2/24 plus 5/9? (Answer: 23/36)

Exact Answer

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Problem: What is 2/24 plus 5/9?
Formula / Expression: 2/24 + 5/9
Final Answer: 23/36
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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 2/24 by 3, and multiply the numerator and denominator of 5/9 by 8 so both fractions share the common base 72.
Working: 2 × 3/24 × 3 = 6/72 and 5 × 8/9 × 8 = 40/72

Step 3: Add the Numerators
Now add the numerators (6 + 40 = 46) and keep the common denominator 72 unchanged.
Working: 6 + 40/72 = 46/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 72, which is 2. Divide both the numerator and denominator by 2.
Working: 46 ÷ 2/72 ÷ 2 = 23/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 36 produces a repeating decimal (approximately 0.638889, or 63.8889%).
Working: 23 ÷ 36 = 0.638889 (63.8889%)

Key Values:
- Simplified Fraction: 23/36
- Mixed Number Form: 23/36
- Decimal Value: 0.638889
- Percentage: 63.8889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-24-plus-5-9/
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2/24 + 5/9 = 23/36

Simplified Fraction

23/36

Mixed Number

Proper (23/36)

Decimal Value

0.638889

Percentage

63.8889%

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Step-by-Step Solution: 2/24 + 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 2/24 by 3, and multiply the numerator and denominator of 5/9 by 8 so both fractions share the common base 72.

2 × 3/24 × 3 = 6/72 and 5 × 8/9 × 8 = 40/72

Step 3

Add the Numerators

Now add the numerators (6 + 40 = 46) and keep the common denominator 72 unchanged.

6 + 40/72 = 46/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 46 and 72, which is 2. Divide both the numerator and denominator by 2.

46 ÷ 2/72 ÷ 2 = 23/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 36 produces a repeating decimal (approximately 0.638889, or 63.8889%).

23 ÷ 36 = 0.638889 (63.8889%)

Visual Representation

The diagram below illustrates 2/24 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/36`
Mixed Number Form	`23/36`
Decimal Form	`0.638889`
Percentage	`63.8889%`

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Frequently Asked Questions

What is 2/24 plus 5/9 as a fraction?

2/24 + 5/9 in simplest fraction form is 23/36.

What is 2/24 plus 5/9 as a decimal?

2/24 + 5/9 converted to a decimal is 0.638889.

What is 2/24 plus 5/9 as a percentage?

2/24 + 5/9 expressed as a percentage is 63.8889%.

Does 2/24 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.638889...) because the denominator contains prime factors other than 2 and 5.