What is 7/27 plus 2/3? (Answer: 25/27)

Exact Answer

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Problem: What is 7/27 plus 2/3?
Formula / Expression: 7/27 + 2/3
Final Answer: 25/27
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 27
Multiply the numerator and denominator of 7/27 by 1, and multiply the numerator and denominator of 2/3 by 9 so both fractions share the common base 27.
Working: 7 × 1/27 × 1 = 7/27 and 2 × 9/3 × 9 = 18/27

Step 3: Add the Numerators
Now add the numerators (7 + 18 = 25) and keep the common denominator 27 unchanged.
Working: 7 + 18/27 = 25/27

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 27 is 1, confirming that 25/27 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 27 produces a repeating decimal (approximately 0.925926, or 92.5926%).
Working: 25 ÷ 27 = 0.925926 (92.5926%)

Key Values:
- Simplified Fraction: 25/27
- Mixed Number Form: 25/27
- Decimal Value: 0.925926
- Percentage: 92.5926%

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Solved with FractionsCalc:
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7/27 + 2/3 = 25/27

Simplified Fraction

25/27

Mixed Number

Proper (25/27)

Decimal Value

0.925926

Percentage

92.5926%

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Step-by-Step Solution: 7/27 + 2/3

Step 1

Find the Least Common Denominator (LCD)

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

LCD(27, 3) = 27

Step 2

Convert to Equivalent Fractions with Common Denominator 27

Multiply the numerator and denominator of 7/27 by 1, and multiply the numerator and denominator of 2/3 by 9 so both fractions share the common base 27.

7 × 1/27 × 1 = 7/27 and 2 × 9/3 × 9 = 18/27

Step 3

Add the Numerators

Now add the numerators (7 + 18 = 25) and keep the common denominator 27 unchanged.

7 + 18/27 = 25/27

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 27 is 1, confirming that 25/27 cannot be reduced further—it is already in its simplest irreducible form.

25/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 27 produces a repeating decimal (approximately 0.925926, or 92.5926%).

25 ÷ 27 = 0.925926 (92.5926%)

Visual Representation

The diagram below illustrates 7/27 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/27`
Mixed Number Form	`25/27`
Decimal Form	`0.925926`
Percentage	`92.5926%`

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Frequently Asked Questions

What is 7/27 plus 2/3 as a fraction?

7/27 + 2/3 in simplest fraction form is 25/27.

What is 7/27 plus 2/3 as a decimal?

7/27 + 2/3 converted to a decimal is 0.925926.

What is 7/27 plus 2/3 as a percentage?

7/27 + 2/3 expressed as a percentage is 92.5926%.

Does 7/27 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.925926...) because the denominator contains prime factors other than 2 and 5.