What is 4/11 plus 5/7? (Answer: 83/77)

Exact Answer

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Problem: What is 4/11 plus 5/7?
Formula / Expression: 4/11 + 5/7
Final Answer: 1 6/77 (83/77)
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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 4/11 by 7, and multiply the numerator and denominator of 5/7 by 11 so both fractions share the common base 77.
Working: 4 × 7/11 × 7 = 28/77 and 5 × 11/7 × 11 = 55/77

Step 3: Add the Numerators
Now add the numerators (28 + 55 = 83) and keep the common denominator 77 unchanged.
Working: 28 + 55/77 = 83/77

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 77 is 1, confirming that 83/77 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/77

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (83) is greater than the denominator (77), divide 83 by 77: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/77.
Working: 83/77 = 1 6/77

Step 6: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 77 produces a repeating decimal (approximately 1.077922, or 107.7922%).
Working: 83 ÷ 77 = 1.077922 (107.7922%)

Key Values:
- Simplified Fraction: 83/77
- Mixed Number Form: 1 6/77
- Decimal Value: 1.077922
- Percentage: 107.7922%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-11-plus-5-7/
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4/11 + 5/7 = 83/77

Simplified Fraction

83/77

Mixed Number

1 6/77

Decimal Value

1.077922

Percentage

107.7922%

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Step-by-Step Solution: 4/11 + 5/7

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 4/11 by 7, and multiply the numerator and denominator of 5/7 by 11 so both fractions share the common base 77.

4 × 7/11 × 7 = 28/77 and 5 × 11/7 × 11 = 55/77

Step 3

Add the Numerators

Now add the numerators (28 + 55 = 83) and keep the common denominator 77 unchanged.

28 + 55/77 = 83/77

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 77 is 1, confirming that 83/77 cannot be reduced further—it is already in its simplest irreducible form.

83/77

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (83) is greater than the denominator (77), divide 83 by 77: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/77.

83/77 = 16/77

Step 6

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 77 produces a repeating decimal (approximately 1.077922, or 107.7922%).

83 ÷ 77 = 1.077922 (107.7922%)

Visual Representation

The diagram below illustrates 4/11 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/77`
Mixed Number Form	`1 6/77`
Decimal Form	`1.077922`
Percentage	`107.7922%`

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Frequently Asked Questions

What is 4/11 plus 5/7 as a fraction?

4/11 + 5/7 in simplest fraction form is 83/77 (or 1 6/77 as a mixed number).

What is 4/11 plus 5/7 as a decimal?

4/11 + 5/7 converted to a decimal is 1.077922.

What is 4/11 plus 5/7 as a percentage?

4/11 + 5/7 expressed as a percentage is 107.7922%.

How do you write 4/11 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 83/77 can be written as the mixed number 1 6/77.

Does 4/11 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.077922...) because the denominator contains prime factors other than 2 and 5.