What is 3/6 plus 6/7? (Answer: 19/14)

Exact Answer

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Problem: What is 3/6 plus 6/7?
Formula / Expression: 3/6 + 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 6 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 7 = 42.
Working: LCD(6, 7) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/6 by 7, and multiply the numerator and denominator of 6/7 by 6 so both fractions share the common base 42.
Working: 3 × 7/6 × 7 = 21/42 and 6 × 6/7 × 6 = 36/42

Step 3: Add the Numerators
Now add the numerators (21 + 36 = 57) and keep the common denominator 42 unchanged.
Working: 21 + 36/42 = 57/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 57 and 42, which is 3. Divide both the numerator and denominator by 3.
Working: 57 ÷ 3/42 ÷ 3 = 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:
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3/6 + 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: 3/6 + 6/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 7 = 42.

LCD(6, 7) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 3/6 by 7, and multiply the numerator and denominator of 6/7 by 6 so both fractions share the common base 42.

3 × 7/6 × 7 = 21/42 and 6 × 6/7 × 6 = 36/42

Step 3

Add the Numerators

Now add the numerators (21 + 36 = 57) and keep the common denominator 42 unchanged.

21 + 36/42 = 57/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 57 and 42, which is 3. Divide both the numerator and denominator by 3.

57 ÷ 3/42 ÷ 3 = 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 3/6 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 3/6 plus 6/7 as a fraction?

3/6 + 6/7 in simplest fraction form is 19/14 (or 1 5/14 as a mixed number).

What is 3/6 plus 6/7 as a decimal?

3/6 + 6/7 converted to a decimal is 1.357143.

What is 3/6 plus 6/7 as a percentage?

3/6 + 6/7 expressed as a percentage is 135.7143%.

How do you write 3/6 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 3/6 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.