What is 2/7 plus 8/11? (Answer: 78/77)

Exact Answer

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Problem: What is 2/7 plus 8/11?
Formula / Expression: 2/7 + 8/11
Final Answer: 1 1/77 (78/77)
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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 2/7 by 11, and multiply the numerator and denominator of 8/11 by 7 so both fractions share the common base 77.
Working: 2 × 11/7 × 11 = 22/77 and 8 × 7/11 × 7 = 56/77

Step 3: Add the Numerators
Now add the numerators (22 + 56 = 78) and keep the common denominator 77 unchanged.
Working: 22 + 56/77 = 78/77

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 78 and 77 is 1, confirming that 78/77 cannot be reduced further—it is already in its simplest irreducible form.
Working: 78/77

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (78) is greater than the denominator (77), divide 78 by 77: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/77.
Working: 78/77 = 1 1/77

Step 6: Decimal & Percentage Representation
Dividing the numerator 78 by denominator 77 produces a repeating decimal (approximately 1.012987, or 101.2987%).
Working: 78 ÷ 77 = 1.012987 (101.2987%)

Key Values:
- Simplified Fraction: 78/77
- Mixed Number Form: 1 1/77
- Decimal Value: 1.012987
- Percentage: 101.2987%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-8-11/
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2/7 + 8/11 = 78/77

Simplified Fraction

78/77

Mixed Number

1 1/77

Decimal Value

1.012987

Percentage

101.2987%

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Step-by-Step Solution: 2/7 + 8/11

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 2/7 by 11, and multiply the numerator and denominator of 8/11 by 7 so both fractions share the common base 77.

2 × 11/7 × 11 = 22/77 and 8 × 7/11 × 7 = 56/77

Step 3

Add the Numerators

Now add the numerators (22 + 56 = 78) and keep the common denominator 77 unchanged.

22 + 56/77 = 78/77

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 78 and 77 is 1, confirming that 78/77 cannot be reduced further—it is already in its simplest irreducible form.

78/77

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (78) is greater than the denominator (77), divide 78 by 77: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/77.

78/77 = 11/77

Step 6

Decimal & Percentage Representation

Dividing the numerator 78 by denominator 77 produces a repeating decimal (approximately 1.012987, or 101.2987%).

78 ÷ 77 = 1.012987 (101.2987%)

Visual Representation

The diagram below illustrates 2/7 plus 8/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`78/77`
Mixed Number Form	`1 1/77`
Decimal Form	`1.012987`
Percentage	`101.2987%`

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Frequently Asked Questions

What is 2/7 plus 8/11 as a fraction?

2/7 + 8/11 in simplest fraction form is 78/77 (or 1 1/77 as a mixed number).

What is 2/7 plus 8/11 as a decimal?

2/7 + 8/11 converted to a decimal is 1.012987.

What is 2/7 plus 8/11 as a percentage?

2/7 + 8/11 expressed as a percentage is 101.2987%.

How do you write 2/7 plus 8/11 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 78/77 can be written as the mixed number 1 1/77.

Does 2/7 plus 8/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.012987...) because the denominator contains prime factors other than 2 and 5.