What is 8/23 plus 2/3? (Answer: 70/69)

Exact Answer

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Problem: What is 8/23 plus 2/3?
Formula / Expression: 8/23 + 2/3
Final Answer: 1 1/69 (70/69)
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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 8/23 by 3, and multiply the numerator and denominator of 2/3 by 23 so both fractions share the common base 69.
Working: 8 × 3/23 × 3 = 24/69 and 2 × 23/3 × 23 = 46/69

Step 3: Add the Numerators
Now add the numerators (24 + 46 = 70) and keep the common denominator 69 unchanged.
Working: 24 + 46/69 = 70/69

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 70 and 69 is 1, confirming that 70/69 cannot be reduced further—it is already in its simplest irreducible form.
Working: 70/69

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (70) is greater than the denominator (69), divide 70 by 69: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/69.
Working: 70/69 = 1 1/69

Step 6: Decimal & Percentage Representation
Dividing the numerator 70 by denominator 69 produces a repeating decimal (approximately 1.014493, or 101.4493%).
Working: 70 ÷ 69 = 1.014493 (101.4493%)

Key Values:
- Simplified Fraction: 70/69
- Mixed Number Form: 1 1/69
- Decimal Value: 1.014493
- Percentage: 101.4493%

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Solved with FractionsCalc:
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8/23 + 2/3 = 70/69

Simplified Fraction

70/69

Mixed Number

1 1/69

Decimal Value

1.014493

Percentage

101.4493%

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Step-by-Step Solution: 8/23 + 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 8/23 by 3, and multiply the numerator and denominator of 2/3 by 23 so both fractions share the common base 69.

8 × 3/23 × 3 = 24/69 and 2 × 23/3 × 23 = 46/69

Step 3

Add the Numerators

Now add the numerators (24 + 46 = 70) and keep the common denominator 69 unchanged.

24 + 46/69 = 70/69

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 70 and 69 is 1, confirming that 70/69 cannot be reduced further—it is already in its simplest irreducible form.

70/69

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (70) is greater than the denominator (69), divide 70 by 69: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/69.

70/69 = 11/69

Step 6

Decimal & Percentage Representation

Dividing the numerator 70 by denominator 69 produces a repeating decimal (approximately 1.014493, or 101.4493%).

70 ÷ 69 = 1.014493 (101.4493%)

Visual Representation

The diagram below illustrates 8/23 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`70/69`
Mixed Number Form	`1 1/69`
Decimal Form	`1.014493`
Percentage	`101.4493%`

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Frequently Asked Questions

What is 8/23 plus 2/3 as a fraction?

8/23 + 2/3 in simplest fraction form is 70/69 (or 1 1/69 as a mixed number).

What is 8/23 plus 2/3 as a decimal?

8/23 + 2/3 converted to a decimal is 1.014493.

What is 8/23 plus 2/3 as a percentage?

8/23 + 2/3 expressed as a percentage is 101.4493%.

How do you write 8/23 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 70/69 can be written as the mixed number 1 1/69.

Does 8/23 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.014493...) because the denominator contains prime factors other than 2 and 5.