What is 1/7 plus 2/11? (Answer: 25/77)

Exact Answer

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Problem: What is 1/7 plus 2/11?
Formula / Expression: 1/7 + 2/11
Final Answer: 25/77
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 11 = 77.
Working: LCD(7, 11) = 77

Step 2: Convert to Equivalent Fractions with Common Denominator 77
Multiply the numerator and denominator of 1/7 by 11, and multiply the numerator and denominator of 2/11 by 7 so both fractions share the common base 77.
Working: 1 × 11/7 × 11 = 11/77 and 2 × 7/11 × 7 = 14/77

Step 3: Add the Numerators
Now add the numerators (11 + 14 = 25) and keep the common denominator 77 unchanged.
Working: 11 + 14/77 = 25/77

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 77 is 1, confirming that 25/77 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 77 produces a repeating decimal (approximately 0.324675, or 32.4675%).
Working: 25 ÷ 77 = 0.324675 (32.4675%)

Key Values:
- Simplified Fraction: 25/77
- Mixed Number Form: 25/77
- Decimal Value: 0.324675
- Percentage: 32.4675%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-2-11/
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1/7 + 2/11 = 25/77

Simplified Fraction

25/77

Mixed Number

Proper (25/77)

Decimal Value

0.324675

Percentage

32.4675%

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Step-by-Step Solution: 1/7 + 2/11

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 11 = 77.

LCD(7, 11) = 77

Step 2

Convert to Equivalent Fractions with Common Denominator 77

Multiply the numerator and denominator of 1/7 by 11, and multiply the numerator and denominator of 2/11 by 7 so both fractions share the common base 77.

1 × 11/7 × 11 = 11/77 and 2 × 7/11 × 7 = 14/77

Step 3

Add the Numerators

Now add the numerators (11 + 14 = 25) and keep the common denominator 77 unchanged.

11 + 14/77 = 25/77

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 77 is 1, confirming that 25/77 cannot be reduced further—it is already in its simplest irreducible form.

25/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 77 produces a repeating decimal (approximately 0.324675, or 32.4675%).

25 ÷ 77 = 0.324675 (32.4675%)

Visual Representation

The diagram below illustrates 1/7 plus 2/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/77`
Mixed Number Form	`25/77`
Decimal Form	`0.324675`
Percentage	`32.4675%`

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Frequently Asked Questions

What is 1/7 plus 2/11 as a fraction?

1/7 + 2/11 in simplest fraction form is 25/77.

What is 1/7 plus 2/11 as a decimal?

1/7 + 2/11 converted to a decimal is 0.324675.

What is 1/7 plus 2/11 as a percentage?

1/7 + 2/11 expressed as a percentage is 32.4675%.

Does 1/7 plus 2/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.324675...) because the denominator contains prime factors other than 2 and 5.