What is 1/11 plus 3/7? (Answer: 40/77)

Exact Answer

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Problem: What is 1/11 plus 3/7?
Formula / Expression: 1/11 + 3/7
Final Answer: 40/77
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 77
Multiply the numerator and denominator of 1/11 by 7, and multiply the numerator and denominator of 3/7 by 11 so both fractions share the common base 77.
Working: 1 × 7/11 × 7 = 7/77 and 3 × 11/7 × 11 = 33/77

Step 3: Add the Numerators
Now add the numerators (7 + 33 = 40) and keep the common denominator 77 unchanged.
Working: 7 + 33/77 = 40/77

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 40 and 77 is 1, confirming that 40/77 cannot be reduced further—it is already in its simplest irreducible form.
Working: 40/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 77 produces a repeating decimal (approximately 0.519481, or 51.9481%).
Working: 40 ÷ 77 = 0.519481 (51.9481%)

Key Values:
- Simplified Fraction: 40/77
- Mixed Number Form: 40/77
- Decimal Value: 0.519481
- Percentage: 51.9481%

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Solved with FractionsCalc:
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1/11 + 3/7 = 40/77

Simplified Fraction

40/77

Mixed Number

Proper (40/77)

Decimal Value

0.519481

Percentage

51.9481%

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Step-by-Step Solution: 1/11 + 3/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(11, 7) = 77

Step 2

Convert to Equivalent Fractions with Common Denominator 77

Multiply the numerator and denominator of 1/11 by 7, and multiply the numerator and denominator of 3/7 by 11 so both fractions share the common base 77.

1 × 7/11 × 7 = 7/77 and 3 × 11/7 × 11 = 33/77

Step 3

Add the Numerators

Now add the numerators (7 + 33 = 40) and keep the common denominator 77 unchanged.

7 + 33/77 = 40/77

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 40 and 77 is 1, confirming that 40/77 cannot be reduced further—it is already in its simplest irreducible form.

40/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 77 produces a repeating decimal (approximately 0.519481, or 51.9481%).

40 ÷ 77 = 0.519481 (51.9481%)

Visual Representation

The diagram below illustrates 1/11 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/77`
Mixed Number Form	`40/77`
Decimal Form	`0.519481`
Percentage	`51.9481%`

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Frequently Asked Questions

What is 1/11 plus 3/7 as a fraction?

1/11 + 3/7 in simplest fraction form is 40/77.

What is 1/11 plus 3/7 as a decimal?

1/11 + 3/7 converted to a decimal is 0.519481.

What is 1/11 plus 3/7 as a percentage?

1/11 + 3/7 expressed as a percentage is 51.9481%.

Does 1/11 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.519481...) because the denominator contains prime factors other than 2 and 5.