What is 3/9 plus 9/24? (Answer: 17/24)

Exact Answer

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Problem: What is 3/9 plus 9/24?
Formula / Expression: 3/9 + 9/24
Final Answer: 17/24
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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 3/9 by 8, and multiply the numerator and denominator of 9/24 by 3 so both fractions share the common base 72.
Working: 3 × 8/9 × 8 = 24/72 and 9 × 3/24 × 3 = 27/72

Step 3: Add the Numerators
Now add the numerators (24 + 27 = 51) and keep the common denominator 72 unchanged.
Working: 24 + 27/72 = 51/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 51 and 72, which is 3. Divide both the numerator and denominator by 3.
Working: 51 ÷ 3/72 ÷ 3 = 17/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 24 produces a repeating decimal (approximately 0.708333, or 70.8333%).
Working: 17 ÷ 24 = 0.708333 (70.8333%)

Key Values:
- Simplified Fraction: 17/24
- Mixed Number Form: 17/24
- Decimal Value: 0.708333
- Percentage: 70.8333%

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Solved with FractionsCalc:
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3/9 + 9/24 = 17/24

Simplified Fraction

17/24

Mixed Number

Proper (17/24)

Decimal Value

0.708333

Percentage

70.8333%

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

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

3 × 8/9 × 8 = 24/72 and 9 × 3/24 × 3 = 27/72

Step 3

Add the Numerators

Now add the numerators (24 + 27 = 51) and keep the common denominator 72 unchanged.

24 + 27/72 = 51/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 51 and 72, which is 3. Divide both the numerator and denominator by 3.

51 ÷ 3/72 ÷ 3 = 17/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 24 produces a repeating decimal (approximately 0.708333, or 70.8333%).

17 ÷ 24 = 0.708333 (70.8333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/24`
Mixed Number Form	`17/24`
Decimal Form	`0.708333`
Percentage	`70.8333%`

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Frequently Asked Questions

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

3/9 + 9/24 in simplest fraction form is 17/24.

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

3/9 + 9/24 converted to a decimal is 0.708333.

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

3/9 + 9/24 expressed as a percentage is 70.8333%.

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

It results in a repeating decimal (approximately 0.708333...) because the denominator contains prime factors other than 2 and 5.