What is 5/24 plus 4/9? (Answer: 47/72)

Exact Answer

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Problem: What is 5/24 plus 4/9?
Formula / Expression: 5/24 + 4/9
Final Answer: 47/72
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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 4/9 by 8 so both fractions share the common base 72.
Working: 5 × 3/24 × 3 = 15/72 and 4 × 8/9 × 8 = 32/72

Step 3: Add the Numerators
Now add the numerators (15 + 32 = 47) and keep the common denominator 72 unchanged.
Working: 15 + 32/72 = 47/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 72 is 1, confirming that 47/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 72 produces a repeating decimal (approximately 0.652778, or 65.2778%).
Working: 47 ÷ 72 = 0.652778 (65.2778%)

Key Values:
- Simplified Fraction: 47/72
- Mixed Number Form: 47/72
- Decimal Value: 0.652778
- Percentage: 65.2778%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-24-plus-4-9/
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5/24 + 4/9 = 47/72

Simplified Fraction

47/72

Mixed Number

Proper (47/72)

Decimal Value

0.652778

Percentage

65.2778%

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Step-by-Step Solution: 5/24 + 4/9

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 4/9 by 8 so both fractions share the common base 72.

5 × 3/24 × 3 = 15/72 and 4 × 8/9 × 8 = 32/72

Step 3

Add the Numerators

Now add the numerators (15 + 32 = 47) and keep the common denominator 72 unchanged.

15 + 32/72 = 47/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 72 is 1, confirming that 47/72 cannot be reduced further—it is already in its simplest irreducible form.

47/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 72 produces a repeating decimal (approximately 0.652778, or 65.2778%).

47 ÷ 72 = 0.652778 (65.2778%)

Visual Representation

The diagram below illustrates 5/24 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/72`
Mixed Number Form	`47/72`
Decimal Form	`0.652778`
Percentage	`65.2778%`

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Frequently Asked Questions

What is 5/24 plus 4/9 as a fraction?

5/24 + 4/9 in simplest fraction form is 47/72.

What is 5/24 plus 4/9 as a decimal?

5/24 + 4/9 converted to a decimal is 0.652778.

What is 5/24 plus 4/9 as a percentage?

5/24 + 4/9 expressed as a percentage is 65.2778%.

Does 5/24 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.652778...) because the denominator contains prime factors other than 2 and 5.