What is 5/24 plus 2/9? (Answer: 31/72)

Exact Answer

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Problem: What is 5/24 plus 2/9?
Formula / Expression: 5/24 + 2/9
Final Answer: 31/72
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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 5/24 by 3, and multiply the numerator and denominator of 2/9 by 8 so both fractions share the common base 72.
Working: 5 × 3/24 × 3 = 15/72 and 2 × 8/9 × 8 = 16/72

Step 3: Add the Numerators
Now add the numerators (15 + 16 = 31) and keep the common denominator 72 unchanged.
Working: 15 + 16/72 = 31/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 72 is 1, confirming that 31/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 72 produces a repeating decimal (approximately 0.430556, or 43.0556%).
Working: 31 ÷ 72 = 0.430556 (43.0556%)

Key Values:
- Simplified Fraction: 31/72
- Mixed Number Form: 31/72
- Decimal Value: 0.430556
- Percentage: 43.0556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-24-plus-2-9/
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5/24 + 2/9 = 31/72

Simplified Fraction

31/72

Mixed Number

Proper (31/72)

Decimal Value

0.430556

Percentage

43.0556%

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Step-by-Step Solution: 5/24 + 2/9

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

5 × 3/24 × 3 = 15/72 and 2 × 8/9 × 8 = 16/72

Step 3

Add the Numerators

Now add the numerators (15 + 16 = 31) and keep the common denominator 72 unchanged.

15 + 16/72 = 31/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 72 is 1, confirming that 31/72 cannot be reduced further—it is already in its simplest irreducible form.

31/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 72 produces a repeating decimal (approximately 0.430556, or 43.0556%).

31 ÷ 72 = 0.430556 (43.0556%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/72`
Mixed Number Form	`31/72`
Decimal Form	`0.430556`
Percentage	`43.0556%`

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Frequently Asked Questions

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

5/24 + 2/9 in simplest fraction form is 31/72.

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

5/24 + 2/9 converted to a decimal is 0.430556.

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

5/24 + 2/9 expressed as a percentage is 43.0556%.

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

It results in a repeating decimal (approximately 0.430556...) because the denominator contains prime factors other than 2 and 5.