What is 2/7 plus 9/23? (Answer: 109/161)

Exact Answer

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Problem: What is 2/7 plus 9/23?
Formula / Expression: 2/7 + 9/23
Final Answer: 109/161
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 23 = 161.
Working: LCD(7, 23) = 161

Step 2: Convert to Equivalent Fractions with Common Denominator 161
Multiply the numerator and denominator of 2/7 by 23, and multiply the numerator and denominator of 9/23 by 7 so both fractions share the common base 161.
Working: 2 × 23/7 × 23 = 46/161 and 9 × 7/23 × 7 = 63/161

Step 3: Add the Numerators
Now add the numerators (46 + 63 = 109) and keep the common denominator 161 unchanged.
Working: 46 + 63/161 = 109/161

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 161 is 1, confirming that 109/161 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 161 produces a repeating decimal (approximately 0.677019, or 67.7019%).
Working: 109 ÷ 161 = 0.677019 (67.7019%)

Key Values:
- Simplified Fraction: 109/161
- Mixed Number Form: 109/161
- Decimal Value: 0.677019
- Percentage: 67.7019%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-9-23/
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2/7 + 9/23 = 109/161

Simplified Fraction

109/161

Mixed Number

Proper (109/161)

Decimal Value

0.677019

Percentage

67.7019%

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Step-by-Step Solution: 2/7 + 9/23

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 23 = 161.

LCD(7, 23) = 161

Step 2

Convert to Equivalent Fractions with Common Denominator 161

Multiply the numerator and denominator of 2/7 by 23, and multiply the numerator and denominator of 9/23 by 7 so both fractions share the common base 161.

2 × 23/7 × 23 = 46/161 and 9 × 7/23 × 7 = 63/161

Step 3

Add the Numerators

Now add the numerators (46 + 63 = 109) and keep the common denominator 161 unchanged.

46 + 63/161 = 109/161

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 161 is 1, confirming that 109/161 cannot be reduced further—it is already in its simplest irreducible form.

109/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 161 produces a repeating decimal (approximately 0.677019, or 67.7019%).

109 ÷ 161 = 0.677019 (67.7019%)

Visual Representation

The diagram below illustrates 2/7 plus 9/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/161`
Mixed Number Form	`109/161`
Decimal Form	`0.677019`
Percentage	`67.7019%`

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Frequently Asked Questions

What is 2/7 plus 9/23 as a fraction?

2/7 + 9/23 in simplest fraction form is 109/161.

What is 2/7 plus 9/23 as a decimal?

2/7 + 9/23 converted to a decimal is 0.677019.

What is 2/7 plus 9/23 as a percentage?

2/7 + 9/23 expressed as a percentage is 67.7019%.

Does 2/7 plus 9/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.677019...) because the denominator contains prime factors other than 2 and 5.