What is 2/9 plus 10/24? (Answer: 23/36)

Exact Answer

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Problem: What is 2/9 plus 10/24?
Formula / Expression: 2/9 + 10/24
Final Answer: 23/36
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 2/9 by 8, and multiply the numerator and denominator of 10/24 by 3 so both fractions share the common base 72.
Working: 2 × 8/9 × 8 = 16/72 and 10 × 3/24 × 3 = 30/72

Step 3: Add the Numerators
Now add the numerators (16 + 30 = 46) and keep the common denominator 72 unchanged.
Working: 16 + 30/72 = 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-2-9-plus-10-24/
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2/9 + 10/24 = 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: 2/9 + 10/24

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 24) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 2/9 by 8, and multiply the numerator and denominator of 10/24 by 3 so both fractions share the common base 72.

2 × 8/9 × 8 = 16/72 and 10 × 3/24 × 3 = 30/72

Step 3

Add the Numerators

Now add the numerators (16 + 30 = 46) and keep the common denominator 72 unchanged.

16 + 30/72 = 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 2/9 plus 10/24 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 2/9 plus 10/24 as a fraction?

2/9 + 10/24 in simplest fraction form is 23/36.

What is 2/9 plus 10/24 as a decimal?

2/9 + 10/24 converted to a decimal is 0.638889.

What is 2/9 plus 10/24 as a percentage?

2/9 + 10/24 expressed as a percentage is 63.8889%.

Does 2/9 plus 10/24 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.