What is 5/23 plus 2/7? (Answer: 81/161)

Exact Answer

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Problem: What is 5/23 plus 2/7?
Formula / Expression: 5/23 + 2/7
Final Answer: 81/161
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 161
Multiply the numerator and denominator of 5/23 by 7, and multiply the numerator and denominator of 2/7 by 23 so both fractions share the common base 161.
Working: 5 × 7/23 × 7 = 35/161 and 2 × 23/7 × 23 = 46/161

Step 3: Add the Numerators
Now add the numerators (35 + 46 = 81) and keep the common denominator 161 unchanged.
Working: 35 + 46/161 = 81/161

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 81 and 161 is 1, confirming that 81/161 cannot be reduced further—it is already in its simplest irreducible form.
Working: 81/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 81 by denominator 161 produces a repeating decimal (approximately 0.503106, or 50.3106%).
Working: 81 ÷ 161 = 0.503106 (50.3106%)

Key Values:
- Simplified Fraction: 81/161
- Mixed Number Form: 81/161
- Decimal Value: 0.503106
- Percentage: 50.3106%

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Solved with FractionsCalc:
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5/23 + 2/7 = 81/161

Simplified Fraction

81/161

Mixed Number

Proper (81/161)

Decimal Value

0.503106

Percentage

50.3106%

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Step-by-Step Solution: 5/23 + 2/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(23, 7) = 161

Step 2

Convert to Equivalent Fractions with Common Denominator 161

Multiply the numerator and denominator of 5/23 by 7, and multiply the numerator and denominator of 2/7 by 23 so both fractions share the common base 161.

5 × 7/23 × 7 = 35/161 and 2 × 23/7 × 23 = 46/161

Step 3

Add the Numerators

Now add the numerators (35 + 46 = 81) and keep the common denominator 161 unchanged.

35 + 46/161 = 81/161

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 81 and 161 is 1, confirming that 81/161 cannot be reduced further—it is already in its simplest irreducible form.

81/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 81 by denominator 161 produces a repeating decimal (approximately 0.503106, or 50.3106%).

81 ÷ 161 = 0.503106 (50.3106%)

Visual Representation

The diagram below illustrates 5/23 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`81/161`
Mixed Number Form	`81/161`
Decimal Form	`0.503106`
Percentage	`50.3106%`

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Frequently Asked Questions

What is 5/23 plus 2/7 as a fraction?

5/23 + 2/7 in simplest fraction form is 81/161.

What is 5/23 plus 2/7 as a decimal?

5/23 + 2/7 converted to a decimal is 0.503106.

What is 5/23 plus 2/7 as a percentage?

5/23 + 2/7 expressed as a percentage is 50.3106%.

Does 5/23 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.503106...) because the denominator contains prime factors other than 2 and 5.