What is 1/24 plus 2/9? (Answer: 19/72)

Exact Answer

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Problem: What is 1/24 plus 2/9?
Formula / Expression: 1/24 + 2/9
Final Answer: 19/72
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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 1/24 by 3, and multiply the numerator and denominator of 2/9 by 8 so both fractions share the common base 72.
Working: 1 × 3/24 × 3 = 3/72 and 2 × 8/9 × 8 = 16/72

Step 3: Add the Numerators
Now add the numerators (3 + 16 = 19) and keep the common denominator 72 unchanged.
Working: 3 + 16/72 = 19/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 72 is 1, confirming that 19/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 72 produces a repeating decimal (approximately 0.263889, or 26.3889%).
Working: 19 ÷ 72 = 0.263889 (26.3889%)

Key Values:
- Simplified Fraction: 19/72
- Mixed Number Form: 19/72
- Decimal Value: 0.263889
- Percentage: 26.3889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-24-plus-2-9/
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1/24 + 2/9 = 19/72

Simplified Fraction

19/72

Mixed Number

Proper (19/72)

Decimal Value

0.263889

Percentage

26.3889%

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Step-by-Step Solution: 1/24 + 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 1/24 by 3, and multiply the numerator and denominator of 2/9 by 8 so both fractions share the common base 72.

1 × 3/24 × 3 = 3/72 and 2 × 8/9 × 8 = 16/72

Step 3

Add the Numerators

Now add the numerators (3 + 16 = 19) and keep the common denominator 72 unchanged.

3 + 16/72 = 19/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 72 is 1, confirming that 19/72 cannot be reduced further—it is already in its simplest irreducible form.

19/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 72 produces a repeating decimal (approximately 0.263889, or 26.3889%).

19 ÷ 72 = 0.263889 (26.3889%)

Visual Representation

The diagram below illustrates 1/24 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/72`
Mixed Number Form	`19/72`
Decimal Form	`0.263889`
Percentage	`26.3889%`

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Frequently Asked Questions

What is 1/24 plus 2/9 as a fraction?

1/24 + 2/9 in simplest fraction form is 19/72.

What is 1/24 plus 2/9 as a decimal?

1/24 + 2/9 converted to a decimal is 0.263889.

What is 1/24 plus 2/9 as a percentage?

1/24 + 2/9 expressed as a percentage is 26.3889%.

Does 1/24 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.263889...) because the denominator contains prime factors other than 2 and 5.