What is 3/24 plus 3/9? (Answer: 11/24)

Exact Answer

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Problem: What is 3/24 plus 3/9?
Formula / Expression: 3/24 + 3/9
Final Answer: 11/24
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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 3/24 by 3, and multiply the numerator and denominator of 3/9 by 8 so both fractions share the common base 72.
Working: 3 × 3/24 × 3 = 9/72 and 3 × 8/9 × 8 = 24/72

Step 3: Add the Numerators
Now add the numerators (9 + 24 = 33) and keep the common denominator 72 unchanged.
Working: 9 + 24/72 = 33/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 72, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/72 ÷ 3 = 11/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 24 produces a repeating decimal (approximately 0.458333, or 45.8333%).
Working: 11 ÷ 24 = 0.458333 (45.8333%)

Key Values:
- Simplified Fraction: 11/24
- Mixed Number Form: 11/24
- Decimal Value: 0.458333
- Percentage: 45.8333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-24-plus-3-9/
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3/24 + 3/9 = 11/24

Simplified Fraction

11/24

Mixed Number

Proper (11/24)

Decimal Value

0.458333

Percentage

45.8333%

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Step-by-Step Solution: 3/24 + 3/9

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

3 × 3/24 × 3 = 9/72 and 3 × 8/9 × 8 = 24/72

Step 3

Add the Numerators

Now add the numerators (9 + 24 = 33) and keep the common denominator 72 unchanged.

9 + 24/72 = 33/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 72, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/72 ÷ 3 = 11/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 24 produces a repeating decimal (approximately 0.458333, or 45.8333%).

11 ÷ 24 = 0.458333 (45.8333%)

Visual Representation

The diagram below illustrates 3/24 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/24`
Mixed Number Form	`11/24`
Decimal Form	`0.458333`
Percentage	`45.8333%`

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Frequently Asked Questions

What is 3/24 plus 3/9 as a fraction?

3/24 + 3/9 in simplest fraction form is 11/24.

What is 3/24 plus 3/9 as a decimal?

3/24 + 3/9 converted to a decimal is 0.458333.

What is 3/24 plus 3/9 as a percentage?

3/24 + 3/9 expressed as a percentage is 45.8333%.

Does 3/24 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.458333...) because the denominator contains prime factors other than 2 and 5.