What is 9/13 plus 5/7? (Answer: 128/91)

Exact Answer

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Problem: What is 9/13 plus 5/7?
Formula / Expression: 9/13 + 5/7
Final Answer: 1 37/91 (128/91)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 9/13 by 7, and multiply the numerator and denominator of 5/7 by 13 so both fractions share the common base 91.
Working: 9 × 7/13 × 7 = 63/91 and 5 × 13/7 × 13 = 65/91

Step 3: Add the Numerators
Now add the numerators (63 + 65 = 128) and keep the common denominator 91 unchanged.
Working: 63 + 65/91 = 128/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 128 and 91 is 1, confirming that 128/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 128/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (128) is greater than the denominator (91), divide 128 by 91: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/91.
Working: 128/91 = 1 37/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 128 by denominator 91 produces a repeating decimal (approximately 1.406593, or 140.6593%).
Working: 128 ÷ 91 = 1.406593 (140.6593%)

Key Values:
- Simplified Fraction: 128/91
- Mixed Number Form: 1 37/91
- Decimal Value: 1.406593
- Percentage: 140.6593%

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Solved with FractionsCalc:
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9/13 + 5/7 = 128/91

Simplified Fraction

128/91

Mixed Number

1 37/91

Decimal Value

1.406593

Percentage

140.6593%

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Step-by-Step Solution: 9/13 + 5/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 7) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 9/13 by 7, and multiply the numerator and denominator of 5/7 by 13 so both fractions share the common base 91.

9 × 7/13 × 7 = 63/91 and 5 × 13/7 × 13 = 65/91

Step 3

Add the Numerators

Now add the numerators (63 + 65 = 128) and keep the common denominator 91 unchanged.

63 + 65/91 = 128/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 128 and 91 is 1, confirming that 128/91 cannot be reduced further—it is already in its simplest irreducible form.

128/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (128) is greater than the denominator (91), divide 128 by 91: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/91.

128/91 = 137/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 128 by denominator 91 produces a repeating decimal (approximately 1.406593, or 140.6593%).

128 ÷ 91 = 1.406593 (140.6593%)

Visual Representation

The diagram below illustrates 9/13 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`128/91`
Mixed Number Form	`1 37/91`
Decimal Form	`1.406593`
Percentage	`140.6593%`

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Frequently Asked Questions

What is 9/13 plus 5/7 as a fraction?

9/13 + 5/7 in simplest fraction form is 128/91 (or 1 37/91 as a mixed number).

What is 9/13 plus 5/7 as a decimal?

9/13 + 5/7 converted to a decimal is 1.406593.

What is 9/13 plus 5/7 as a percentage?

9/13 + 5/7 expressed as a percentage is 140.6593%.

How do you write 9/13 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 128/91 can be written as the mixed number 1 37/91.

Does 9/13 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.406593...) because the denominator contains prime factors other than 2 and 5.