What is 10/23 plus 2/3? (Answer: 76/69)

Exact Answer

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Problem: What is 10/23 plus 2/3?
Formula / Expression: 10/23 + 2/3
Final Answer: 1 7/69 (76/69)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 3 = 69.
Working: LCD(23, 3) = 69

Step 2: Convert to Equivalent Fractions with Common Denominator 69
Multiply the numerator and denominator of 10/23 by 3, and multiply the numerator and denominator of 2/3 by 23 so both fractions share the common base 69.
Working: 10 × 3/23 × 3 = 30/69 and 2 × 23/3 × 23 = 46/69

Step 3: Add the Numerators
Now add the numerators (30 + 46 = 76) and keep the common denominator 69 unchanged.
Working: 30 + 46/69 = 76/69

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 69 is 1, confirming that 76/69 cannot be reduced further—it is already in its simplest irreducible form.
Working: 76/69

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (76) is greater than the denominator (69), divide 76 by 69: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/69.
Working: 76/69 = 1 7/69

Step 6: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 69 produces a repeating decimal (approximately 1.101449, or 110.1449%).
Working: 76 ÷ 69 = 1.101449 (110.1449%)

Key Values:
- Simplified Fraction: 76/69
- Mixed Number Form: 1 7/69
- Decimal Value: 1.101449
- Percentage: 110.1449%

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Solved with FractionsCalc:
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10/23 + 2/3 = 76/69

Simplified Fraction

76/69

Mixed Number

1 7/69

Decimal Value

1.101449

Percentage

110.1449%

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Step-by-Step Solution: 10/23 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 3 = 69.

LCD(23, 3) = 69

Step 2

Convert to Equivalent Fractions with Common Denominator 69

Multiply the numerator and denominator of 10/23 by 3, and multiply the numerator and denominator of 2/3 by 23 so both fractions share the common base 69.

10 × 3/23 × 3 = 30/69 and 2 × 23/3 × 23 = 46/69

Step 3

Add the Numerators

Now add the numerators (30 + 46 = 76) and keep the common denominator 69 unchanged.

30 + 46/69 = 76/69

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 76 and 69 is 1, confirming that 76/69 cannot be reduced further—it is already in its simplest irreducible form.

76/69

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (76) is greater than the denominator (69), divide 76 by 69: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/69.

76/69 = 17/69

Step 6

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 69 produces a repeating decimal (approximately 1.101449, or 110.1449%).

76 ÷ 69 = 1.101449 (110.1449%)

Visual Representation

The diagram below illustrates 10/23 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/69`
Mixed Number Form	`1 7/69`
Decimal Form	`1.101449`
Percentage	`110.1449%`

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Frequently Asked Questions

What is 10/23 plus 2/3 as a fraction?

10/23 + 2/3 in simplest fraction form is 76/69 (or 1 7/69 as a mixed number).

What is 10/23 plus 2/3 as a decimal?

10/23 + 2/3 converted to a decimal is 1.101449.

What is 10/23 plus 2/3 as a percentage?

10/23 + 2/3 expressed as a percentage is 110.1449%.

How do you write 10/23 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 76/69 can be written as the mixed number 1 7/69.

Does 10/23 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.101449...) because the denominator contains prime factors other than 2 and 5.