What is 8/14 plus 2/3? (Answer: 26/21)

Exact Answer

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Problem: What is 8/14 plus 2/3?
Formula / Expression: 8/14 + 2/3
Final Answer: 1 5/21 (26/21)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 3 = 42.
Working: LCD(14, 3) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 8/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.
Working: 8 × 3/14 × 3 = 24/42 and 2 × 14/3 × 14 = 28/42

Step 3: Add the Numerators
Now add the numerators (24 + 28 = 52) and keep the common denominator 42 unchanged.
Working: 24 + 28/42 = 52/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 52 and 42, which is 2. Divide both the numerator and denominator by 2.
Working: 52 ÷ 2/42 ÷ 2 = 26/21

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (26) is greater than the denominator (21), divide 26 by 21: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/21.
Working: 26/21 = 1 5/21

Step 6: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 21 produces a repeating decimal (approximately 1.238095, or 123.8095%).
Working: 26 ÷ 21 = 1.238095 (123.8095%)

Key Values:
- Simplified Fraction: 26/21
- Mixed Number Form: 1 5/21
- Decimal Value: 1.238095
- Percentage: 123.8095%

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Solved with FractionsCalc:
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8/14 + 2/3 = 26/21

Simplified Fraction

26/21

Mixed Number

1 5/21

Decimal Value

1.238095

Percentage

123.8095%

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Step-by-Step Solution: 8/14 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 3 = 42.

LCD(14, 3) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 8/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.

8 × 3/14 × 3 = 24/42 and 2 × 14/3 × 14 = 28/42

Step 3

Add the Numerators

Now add the numerators (24 + 28 = 52) and keep the common denominator 42 unchanged.

24 + 28/42 = 52/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 52 and 42, which is 2. Divide both the numerator and denominator by 2.

52 ÷ 2/42 ÷ 2 = 26/21

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (26) is greater than the denominator (21), divide 26 by 21: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/21.

26/21 = 15/21

Step 6

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 21 produces a repeating decimal (approximately 1.238095, or 123.8095%).

26 ÷ 21 = 1.238095 (123.8095%)

Visual Representation

The diagram below illustrates 8/14 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/21`
Mixed Number Form	`1 5/21`
Decimal Form	`1.238095`
Percentage	`123.8095%`

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Frequently Asked Questions

What is 8/14 plus 2/3 as a fraction?

8/14 + 2/3 in simplest fraction form is 26/21 (or 1 5/21 as a mixed number).

What is 8/14 plus 2/3 as a decimal?

8/14 + 2/3 converted to a decimal is 1.238095.

What is 8/14 plus 2/3 as a percentage?

8/14 + 2/3 expressed as a percentage is 123.8095%.

How do you write 8/14 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 26/21 can be written as the mixed number 1 5/21.

Does 8/14 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.238095...) because the denominator contains prime factors other than 2 and 5.