What is 1/2 plus 6/7? (Answer: 19/14)

Exact Answer

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Problem: What is 1/2 plus 6/7?
Formula / Expression: 1/2 + 6/7
Final Answer: 1 5/14 (19/14)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 2 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 7 = 14.
Working: LCD(2, 7) = 14

Step 2: Convert to Equivalent Fractions with Common Denominator 14
Multiply the numerator and denominator of 1/2 by 7, and multiply the numerator and denominator of 6/7 by 2 so both fractions share the common base 14.
Working: 1 × 7/2 × 7 = 7/14 and 6 × 2/7 × 2 = 12/14

Step 3: Add the Numerators
Now add the numerators (7 + 12 = 19) and keep the common denominator 14 unchanged.
Working: 7 + 12/14 = 19/14

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 14 is 1, confirming that 19/14 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (19) is greater than the denominator (14), divide 19 by 14: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/14.
Working: 19/14 = 1 5/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 14 produces a repeating decimal (approximately 1.357143, or 135.7143%).
Working: 19 ÷ 14 = 1.357143 (135.7143%)

Key Values:
- Simplified Fraction: 19/14
- Mixed Number Form: 1 5/14
- Decimal Value: 1.357143
- Percentage: 135.7143%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-6-7/
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1/2 + 6/7 = 19/14

Simplified Fraction

19/14

Mixed Number

1 5/14

Decimal Value

1.357143

Percentage

135.7143%

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Step-by-Step Solution: 1/2 + 6/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 2 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 7 = 14.

LCD(2, 7) = 14

Step 2

Convert to Equivalent Fractions with Common Denominator 14

Multiply the numerator and denominator of 1/2 by 7, and multiply the numerator and denominator of 6/7 by 2 so both fractions share the common base 14.

1 × 7/2 × 7 = 7/14 and 6 × 2/7 × 2 = 12/14

Step 3

Add the Numerators

Now add the numerators (7 + 12 = 19) and keep the common denominator 14 unchanged.

7 + 12/14 = 19/14

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 14 is 1, confirming that 19/14 cannot be reduced further—it is already in its simplest irreducible form.

19/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (19) is greater than the denominator (14), divide 19 by 14: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/14.

19/14 = 15/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 14 produces a repeating decimal (approximately 1.357143, or 135.7143%).

19 ÷ 14 = 1.357143 (135.7143%)

Visual Representation

The diagram below illustrates 1/2 plus 6/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/14`
Mixed Number Form	`1 5/14`
Decimal Form	`1.357143`
Percentage	`135.7143%`

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Frequently Asked Questions

What is 1/2 plus 6/7 as a fraction?

1/2 + 6/7 in simplest fraction form is 19/14 (or 1 5/14 as a mixed number).

What is 1/2 plus 6/7 as a decimal?

1/2 + 6/7 converted to a decimal is 1.357143.

What is 1/2 plus 6/7 as a percentage?

1/2 + 6/7 expressed as a percentage is 135.7143%.

How do you write 1/2 plus 6/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 19/14 can be written as the mixed number 1 5/14.

Does 1/2 plus 6/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.357143...) because the denominator contains prime factors other than 2 and 5.