What is 4/7 plus 8/13? (Answer: 108/91)

Exact Answer

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Problem: What is 4/7 plus 8/13?
Formula / Expression: 4/7 + 8/13
Final Answer: 1 17/91 (108/91)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 13 = 91.
Working: LCD(7, 13) = 91

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 4/7 by 13, and multiply the numerator and denominator of 8/13 by 7 so both fractions share the common base 91.
Working: 4 × 13/7 × 13 = 52/91 and 8 × 7/13 × 7 = 56/91

Step 3: Add the Numerators
Now add the numerators (52 + 56 = 108) and keep the common denominator 91 unchanged.
Working: 52 + 56/91 = 108/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 108 and 91 is 1, confirming that 108/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 108/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (108) is greater than the denominator (91), divide 108 by 91: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/91.
Working: 108/91 = 1 17/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 108 by denominator 91 produces a repeating decimal (approximately 1.186813, or 118.6813%).
Working: 108 ÷ 91 = 1.186813 (118.6813%)

Key Values:
- Simplified Fraction: 108/91
- Mixed Number Form: 1 17/91
- Decimal Value: 1.186813
- Percentage: 118.6813%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-7-plus-8-13/
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4/7 + 8/13 = 108/91

Simplified Fraction

108/91

Mixed Number

1 17/91

Decimal Value

1.186813

Percentage

118.6813%

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Step-by-Step Solution: 4/7 + 8/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 13 = 91.

LCD(7, 13) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 4/7 by 13, and multiply the numerator and denominator of 8/13 by 7 so both fractions share the common base 91.

4 × 13/7 × 13 = 52/91 and 8 × 7/13 × 7 = 56/91

Step 3

Add the Numerators

Now add the numerators (52 + 56 = 108) and keep the common denominator 91 unchanged.

52 + 56/91 = 108/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 108 and 91 is 1, confirming that 108/91 cannot be reduced further—it is already in its simplest irreducible form.

108/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (108) is greater than the denominator (91), divide 108 by 91: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/91.

108/91 = 117/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 108 by denominator 91 produces a repeating decimal (approximately 1.186813, or 118.6813%).

108 ÷ 91 = 1.186813 (118.6813%)

Visual Representation

The diagram below illustrates 4/7 plus 8/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`108/91`
Mixed Number Form	`1 17/91`
Decimal Form	`1.186813`
Percentage	`118.6813%`

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Frequently Asked Questions

What is 4/7 plus 8/13 as a fraction?

4/7 + 8/13 in simplest fraction form is 108/91 (or 1 17/91 as a mixed number).

What is 4/7 plus 8/13 as a decimal?

4/7 + 8/13 converted to a decimal is 1.186813.

What is 4/7 plus 8/13 as a percentage?

4/7 + 8/13 expressed as a percentage is 118.6813%.

How do you write 4/7 plus 8/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 108/91 can be written as the mixed number 1 17/91.

Does 4/7 plus 8/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.186813...) because the denominator contains prime factors other than 2 and 5.