What is 2/7 plus 9/27? (Answer: 13/21)

Exact Answer

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Problem: What is 2/7 plus 9/27?
Formula / Expression: 2/7 + 9/27
Final Answer: 13/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 27 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 27 = 189.
Working: LCD(7, 27) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 2/7 by 27, and multiply the numerator and denominator of 9/27 by 7 so both fractions share the common base 189.
Working: 2 × 27/7 × 27 = 54/189 and 9 × 7/27 × 7 = 63/189

Step 3: Add the Numerators
Now add the numerators (54 + 63 = 117) and keep the common denominator 189 unchanged.
Working: 54 + 63/189 = 117/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 117 and 189, which is 9. Divide both the numerator and denominator by 9.
Working: 117 ÷ 9/189 ÷ 9 = 13/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).
Working: 13 ÷ 21 = 0.619048 (61.9048%)

Key Values:
- Simplified Fraction: 13/21
- Mixed Number Form: 13/21
- Decimal Value: 0.619048
- Percentage: 61.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-9-27/
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2/7 + 9/27 = 13/21

Simplified Fraction

13/21

Mixed Number

Proper (13/21)

Decimal Value

0.619048

Percentage

61.9048%

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Step-by-Step Solution: 2/7 + 9/27

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 27 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 27 = 189.

LCD(7, 27) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 2/7 by 27, and multiply the numerator and denominator of 9/27 by 7 so both fractions share the common base 189.

2 × 27/7 × 27 = 54/189 and 9 × 7/27 × 7 = 63/189

Step 3

Add the Numerators

Now add the numerators (54 + 63 = 117) and keep the common denominator 189 unchanged.

54 + 63/189 = 117/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 117 and 189, which is 9. Divide both the numerator and denominator by 9.

117 ÷ 9/189 ÷ 9 = 13/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).

13 ÷ 21 = 0.619048 (61.9048%)

Visual Representation

The diagram below illustrates 2/7 plus 9/27 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/21`
Mixed Number Form	`13/21`
Decimal Form	`0.619048`
Percentage	`61.9048%`

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Frequently Asked Questions

What is 2/7 plus 9/27 as a fraction?

2/7 + 9/27 in simplest fraction form is 13/21.

What is 2/7 plus 9/27 as a decimal?

2/7 + 9/27 converted to a decimal is 0.619048.

What is 2/7 plus 9/27 as a percentage?

2/7 + 9/27 expressed as a percentage is 61.9048%.

Does 2/7 plus 9/27 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.619048...) because the denominator contains prime factors other than 2 and 5.