What is 3/23 plus 2/7? (Answer: 67/161)

Exact Answer

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Problem: What is 3/23 plus 2/7?
Formula / Expression: 3/23 + 2/7
Final Answer: 67/161
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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 3/23 by 7, and multiply the numerator and denominator of 2/7 by 23 so both fractions share the common base 161.
Working: 3 × 7/23 × 7 = 21/161 and 2 × 23/7 × 23 = 46/161

Step 3: Add the Numerators
Now add the numerators (21 + 46 = 67) and keep the common denominator 161 unchanged.
Working: 21 + 46/161 = 67/161

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 161 is 1, confirming that 67/161 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 161 produces a repeating decimal (approximately 0.416149, or 41.6149%).
Working: 67 ÷ 161 = 0.416149 (41.6149%)

Key Values:
- Simplified Fraction: 67/161
- Mixed Number Form: 67/161
- Decimal Value: 0.416149
- Percentage: 41.6149%

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Solved with FractionsCalc:
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3/23 + 2/7 = 67/161

Simplified Fraction

67/161

Mixed Number

Proper (67/161)

Decimal Value

0.416149

Percentage

41.6149%

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Step-by-Step Solution: 3/23 + 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 3/23 by 7, and multiply the numerator and denominator of 2/7 by 23 so both fractions share the common base 161.

3 × 7/23 × 7 = 21/161 and 2 × 23/7 × 23 = 46/161

Step 3

Add the Numerators

Now add the numerators (21 + 46 = 67) and keep the common denominator 161 unchanged.

21 + 46/161 = 67/161

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 161 is 1, confirming that 67/161 cannot be reduced further—it is already in its simplest irreducible form.

67/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 161 produces a repeating decimal (approximately 0.416149, or 41.6149%).

67 ÷ 161 = 0.416149 (41.6149%)

Visual Representation

The diagram below illustrates 3/23 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/161`
Mixed Number Form	`67/161`
Decimal Form	`0.416149`
Percentage	`41.6149%`

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Frequently Asked Questions

What is 3/23 plus 2/7 as a fraction?

3/23 + 2/7 in simplest fraction form is 67/161.

What is 3/23 plus 2/7 as a decimal?

3/23 + 2/7 converted to a decimal is 0.416149.

What is 3/23 plus 2/7 as a percentage?

3/23 + 2/7 expressed as a percentage is 41.6149%.

Does 3/23 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.416149...) because the denominator contains prime factors other than 2 and 5.