What is 1/5 plus 6/7? (Answer: 37/35)

Exact Answer

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Problem: What is 1/5 plus 6/7?
Formula / Expression: 1/5 + 6/7
Final Answer: 1 2/35 (37/35)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 7 = 35.
Working: LCD(5, 7) = 35

Step 2: Convert to Equivalent Fractions with Common Denominator 35
Multiply the numerator and denominator of 1/5 by 7, and multiply the numerator and denominator of 6/7 by 5 so both fractions share the common base 35.
Working: 1 × 7/5 × 7 = 7/35 and 6 × 5/7 × 5 = 30/35

Step 3: Add the Numerators
Now add the numerators (7 + 30 = 37) and keep the common denominator 35 unchanged.
Working: 7 + 30/35 = 37/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 35 is 1, confirming that 37/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (37) is greater than the denominator (35), divide 37 by 35: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/35.
Working: 37/35 = 1 2/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 35 produces a repeating decimal (approximately 1.057143, or 105.7143%).
Working: 37 ÷ 35 = 1.057143 (105.7143%)

Key Values:
- Simplified Fraction: 37/35
- Mixed Number Form: 1 2/35
- Decimal Value: 1.057143
- Percentage: 105.7143%

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Solved with FractionsCalc:
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1/5 + 6/7 = 37/35

Simplified Fraction

37/35

Mixed Number

1 2/35

Decimal Value

1.057143

Percentage

105.7143%

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Step-by-Step Solution: 1/5 + 6/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 7 = 35.

LCD(5, 7) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

Multiply the numerator and denominator of 1/5 by 7, and multiply the numerator and denominator of 6/7 by 5 so both fractions share the common base 35.

1 × 7/5 × 7 = 7/35 and 6 × 5/7 × 5 = 30/35

Step 3

Add the Numerators

Now add the numerators (7 + 30 = 37) and keep the common denominator 35 unchanged.

7 + 30/35 = 37/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 35 is 1, confirming that 37/35 cannot be reduced further—it is already in its simplest irreducible form.

37/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (37) is greater than the denominator (35), divide 37 by 35: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/35.

37/35 = 12/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 35 produces a repeating decimal (approximately 1.057143, or 105.7143%).

37 ÷ 35 = 1.057143 (105.7143%)

Visual Representation

The diagram below illustrates 1/5 plus 6/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/35`
Mixed Number Form	`1 2/35`
Decimal Form	`1.057143`
Percentage	`105.7143%`

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Frequently Asked Questions

What is 1/5 plus 6/7 as a fraction?

1/5 + 6/7 in simplest fraction form is 37/35 (or 1 2/35 as a mixed number).

What is 1/5 plus 6/7 as a decimal?

1/5 + 6/7 converted to a decimal is 1.057143.

What is 1/5 plus 6/7 as a percentage?

1/5 + 6/7 expressed as a percentage is 105.7143%.

How do you write 1/5 plus 6/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 37/35 can be written as the mixed number 1 2/35.

Does 1/5 plus 6/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.057143...) because the denominator contains prime factors other than 2 and 5.