What is 5/7 plus 11/13? (Answer: 142/91)

Exact Answer

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Problem: What is 5/7 plus 11/13?
Formula / Expression: 5/7 + 11/13
Final Answer: 1 51/91 (142/91)
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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 5/7 by 13, and multiply the numerator and denominator of 11/13 by 7 so both fractions share the common base 91.
Working: 5 × 13/7 × 13 = 65/91 and 11 × 7/13 × 7 = 77/91

Step 3: Add the Numerators
Now add the numerators (65 + 77 = 142) and keep the common denominator 91 unchanged.
Working: 65 + 77/91 = 142/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 142 and 91 is 1, confirming that 142/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 142/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (142) is greater than the denominator (91), divide 142 by 91: it goes in 1 whole time(s) with a remainder of 51, giving the mixed number 1 51/91.
Working: 142/91 = 1 51/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 142 by denominator 91 produces a repeating decimal (approximately 1.56044, or 156.044%).
Working: 142 ÷ 91 = 1.56044 (156.044%)

Key Values:
- Simplified Fraction: 142/91
- Mixed Number Form: 1 51/91
- Decimal Value: 1.56044
- Percentage: 156.044%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-7-plus-11-13/
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5/7 + 11/13 = 142/91

Simplified Fraction

142/91

Mixed Number

1 51/91

Decimal Value

1.56044

Percentage

156.044%

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Step-by-Step Solution: 5/7 + 11/13

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 5/7 by 13, and multiply the numerator and denominator of 11/13 by 7 so both fractions share the common base 91.

5 × 13/7 × 13 = 65/91 and 11 × 7/13 × 7 = 77/91

Step 3

Add the Numerators

Now add the numerators (65 + 77 = 142) and keep the common denominator 91 unchanged.

65 + 77/91 = 142/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 142 and 91 is 1, confirming that 142/91 cannot be reduced further—it is already in its simplest irreducible form.

142/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (142) is greater than the denominator (91), divide 142 by 91: it goes in 1 whole time(s) with a remainder of 51, giving the mixed number 1 51/91.

142/91 = 151/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 142 by denominator 91 produces a repeating decimal (approximately 1.56044, or 156.044%).

142 ÷ 91 = 1.56044 (156.044%)

Visual Representation

The diagram below illustrates 5/7 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`142/91`
Mixed Number Form	`1 51/91`
Decimal Form	`1.56044`
Percentage	`156.044%`

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Frequently Asked Questions

What is 5/7 plus 11/13 as a fraction?

5/7 + 11/13 in simplest fraction form is 142/91 (or 1 51/91 as a mixed number).

What is 5/7 plus 11/13 as a decimal?

5/7 + 11/13 converted to a decimal is 1.56044.

What is 5/7 plus 11/13 as a percentage?

5/7 + 11/13 expressed as a percentage is 156.044%.

How do you write 5/7 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 142/91 can be written as the mixed number 1 51/91.

Does 5/7 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.56044...) because the denominator contains prime factors other than 2 and 5.