What is 2/7 plus 10/23? (Answer: 116/161)

Exact Answer

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Problem: What is 2/7 plus 10/23?
Formula / Expression: 2/7 + 10/23
Final Answer: 116/161
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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 10/23 by 7 so both fractions share the common base 161.
Working: 2 × 23/7 × 23 = 46/161 and 10 × 7/23 × 7 = 70/161

Step 3: Add the Numerators
Now add the numerators (46 + 70 = 116) and keep the common denominator 161 unchanged.
Working: 46 + 70/161 = 116/161

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 116 and 161 is 1, confirming that 116/161 cannot be reduced further—it is already in its simplest irreducible form.
Working: 116/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 116 by denominator 161 produces a repeating decimal (approximately 0.720497, or 72.0497%).
Working: 116 ÷ 161 = 0.720497 (72.0497%)

Key Values:
- Simplified Fraction: 116/161
- Mixed Number Form: 116/161
- Decimal Value: 0.720497
- Percentage: 72.0497%

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Solved with FractionsCalc:
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2/7 + 10/23 = 116/161

Simplified Fraction

116/161

Mixed Number

Proper (116/161)

Decimal Value

0.720497

Percentage

72.0497%

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Step-by-Step Solution: 2/7 + 10/23

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 10/23 by 7 so both fractions share the common base 161.

2 × 23/7 × 23 = 46/161 and 10 × 7/23 × 7 = 70/161

Step 3

Add the Numerators

Now add the numerators (46 + 70 = 116) and keep the common denominator 161 unchanged.

46 + 70/161 = 116/161

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 116 and 161 is 1, confirming that 116/161 cannot be reduced further—it is already in its simplest irreducible form.

116/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 116 by denominator 161 produces a repeating decimal (approximately 0.720497, or 72.0497%).

116 ÷ 161 = 0.720497 (72.0497%)

Visual Representation

The diagram below illustrates 2/7 plus 10/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`116/161`
Mixed Number Form	`116/161`
Decimal Form	`0.720497`
Percentage	`72.0497%`

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Frequently Asked Questions

What is 2/7 plus 10/23 as a fraction?

2/7 + 10/23 in simplest fraction form is 116/161.

What is 2/7 plus 10/23 as a decimal?

2/7 + 10/23 converted to a decimal is 0.720497.

What is 2/7 plus 10/23 as a percentage?

2/7 + 10/23 expressed as a percentage is 72.0497%.

Does 2/7 plus 10/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.720497...) because the denominator contains prime factors other than 2 and 5.