What is 4/27 plus 4/9? (Answer: 16/27)

Exact Answer

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Problem: What is 4/27 plus 4/9?
Formula / Expression: 4/27 + 4/9
Final Answer: 16/27
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 27 is an exact multiple of 9 (9 × 3 = 27). The Least Common Denominator (LCD) is simply 27, meaning we only need to scale one fraction.
Working: LCD(27, 9) = 27

Step 2: Convert to Equivalent Fractions with Common Denominator 27
Multiply the numerator and denominator of 4/27 by 1, and multiply the numerator and denominator of 4/9 by 3 so both fractions share the common base 27.
Working: 4 × 1/27 × 1 = 4/27 and 4 × 3/9 × 3 = 12/27

Step 3: Add the Numerators
Now add the numerators (4 + 12 = 16) and keep the common denominator 27 unchanged.
Working: 4 + 12/27 = 16/27

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 16 and 27 is 1, confirming that 16/27 cannot be reduced further—it is already in its simplest irreducible form.
Working: 16/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 27 produces a repeating decimal (approximately 0.592593, or 59.2593%).
Working: 16 ÷ 27 = 0.592593 (59.2593%)

Key Values:
- Simplified Fraction: 16/27
- Mixed Number Form: 16/27
- Decimal Value: 0.592593
- Percentage: 59.2593%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-27-plus-4-9/
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4/27 + 4/9 = 16/27

Simplified Fraction

16/27

Mixed Number

Proper (16/27)

Decimal Value

0.592593

Percentage

59.2593%

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Step-by-Step Solution: 4/27 + 4/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 27 is an exact multiple of 9 (9 × 3 = 27). The Least Common Denominator (LCD) is simply 27, meaning we only need to scale one fraction.

LCD(27, 9) = 27

Step 2

Convert to Equivalent Fractions with Common Denominator 27

Multiply the numerator and denominator of 4/27 by 1, and multiply the numerator and denominator of 4/9 by 3 so both fractions share the common base 27.

4 × 1/27 × 1 = 4/27 and 4 × 3/9 × 3 = 12/27

Step 3

Add the Numerators

Now add the numerators (4 + 12 = 16) and keep the common denominator 27 unchanged.

4 + 12/27 = 16/27

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 16 and 27 is 1, confirming that 16/27 cannot be reduced further—it is already in its simplest irreducible form.

16/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 27 produces a repeating decimal (approximately 0.592593, or 59.2593%).

16 ÷ 27 = 0.592593 (59.2593%)

Visual Representation

The diagram below illustrates 4/27 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/27`
Mixed Number Form	`16/27`
Decimal Form	`0.592593`
Percentage	`59.2593%`

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Frequently Asked Questions

What is 4/27 plus 4/9 as a fraction?

4/27 + 4/9 in simplest fraction form is 16/27.

What is 4/27 plus 4/9 as a decimal?

4/27 + 4/9 converted to a decimal is 0.592593.

What is 4/27 plus 4/9 as a percentage?

4/27 + 4/9 expressed as a percentage is 59.2593%.

Does 4/27 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.592593...) because the denominator contains prime factors other than 2 and 5.