What is 1/6 plus 2/7? (Answer: 19/42)

Exact Answer

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Problem: What is 1/6 plus 2/7?
Formula / Expression: 1/6 + 2/7
Final Answer: 19/42
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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 1/6 by 7, and multiply the numerator and denominator of 2/7 by 6 so both fractions share the common base 42.
Working: 1 × 7/6 × 7 = 7/42 and 2 × 6/7 × 6 = 12/42

Step 3: Add the Numerators
Now add the numerators (7 + 12 = 19) and keep the common denominator 42 unchanged.
Working: 7 + 12/42 = 19/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 42 is 1, confirming that 19/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).
Working: 19 ÷ 42 = 0.452381 (45.2381%)

Key Values:
- Simplified Fraction: 19/42
- Mixed Number Form: 19/42
- Decimal Value: 0.452381
- Percentage: 45.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-6-plus-2-7/
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1/6 + 2/7 = 19/42

Simplified Fraction

19/42

Mixed Number

Proper (19/42)

Decimal Value

0.452381

Percentage

45.2381%

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

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 1/6 by 7, and multiply the numerator and denominator of 2/7 by 6 so both fractions share the common base 42.

1 × 7/6 × 7 = 7/42 and 2 × 6/7 × 6 = 12/42

Step 3

Add the Numerators

Now add the numerators (7 + 12 = 19) and keep the common denominator 42 unchanged.

7 + 12/42 = 19/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 42 is 1, confirming that 19/42 cannot be reduced further—it is already in its simplest irreducible form.

19/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).

19 ÷ 42 = 0.452381 (45.2381%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/42`
Mixed Number Form	`19/42`
Decimal Form	`0.452381`
Percentage	`45.2381%`

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Frequently Asked Questions

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

1/6 + 2/7 in simplest fraction form is 19/42.

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

1/6 + 2/7 converted to a decimal is 0.452381.

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

1/6 + 2/7 expressed as a percentage is 45.2381%.

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

It results in a repeating decimal (approximately 0.452381...) because the denominator contains prime factors other than 2 and 5.