What is 3/11 plus 4/7? (Answer: 65/77)

Exact Answer

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Problem: What is 3/11 plus 4/7?
Formula / Expression: 3/11 + 4/7
Final Answer: 65/77
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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 3/11 by 7, and multiply the numerator and denominator of 4/7 by 11 so both fractions share the common base 77.
Working: 3 × 7/11 × 7 = 21/77 and 4 × 11/7 × 11 = 44/77

Step 3: Add the Numerators
Now add the numerators (21 + 44 = 65) and keep the common denominator 77 unchanged.
Working: 21 + 44/77 = 65/77

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 65 and 77 is 1, confirming that 65/77 cannot be reduced further—it is already in its simplest irreducible form.
Working: 65/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 77 produces a repeating decimal (approximately 0.844156, or 84.4156%).
Working: 65 ÷ 77 = 0.844156 (84.4156%)

Key Values:
- Simplified Fraction: 65/77
- Mixed Number Form: 65/77
- Decimal Value: 0.844156
- Percentage: 84.4156%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-11-plus-4-7/
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3/11 + 4/7 = 65/77

Simplified Fraction

65/77

Mixed Number

Proper (65/77)

Decimal Value

0.844156

Percentage

84.4156%

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Step-by-Step Solution: 3/11 + 4/7

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 3/11 by 7, and multiply the numerator and denominator of 4/7 by 11 so both fractions share the common base 77.

3 × 7/11 × 7 = 21/77 and 4 × 11/7 × 11 = 44/77

Step 3

Add the Numerators

Now add the numerators (21 + 44 = 65) and keep the common denominator 77 unchanged.

21 + 44/77 = 65/77

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 65 and 77 is 1, confirming that 65/77 cannot be reduced further—it is already in its simplest irreducible form.

65/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 77 produces a repeating decimal (approximately 0.844156, or 84.4156%).

65 ÷ 77 = 0.844156 (84.4156%)

Visual Representation

The diagram below illustrates 3/11 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/77`
Mixed Number Form	`65/77`
Decimal Form	`0.844156`
Percentage	`84.4156%`

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Frequently Asked Questions

What is 3/11 plus 4/7 as a fraction?

3/11 + 4/7 in simplest fraction form is 65/77.

What is 3/11 plus 4/7 as a decimal?

3/11 + 4/7 converted to a decimal is 0.844156.

What is 3/11 plus 4/7 as a percentage?

3/11 + 4/7 expressed as a percentage is 84.4156%.

Does 3/11 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.844156...) because the denominator contains prime factors other than 2 and 5.