What is 7/13 plus 5/9? (Answer: 128/117)

Exact Answer

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Problem: What is 7/13 plus 5/9?
Formula / Expression: 7/13 + 5/9
Final Answer: 1 11/117 (128/117)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 9 = 117.
Working: LCD(13, 9) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 7/13 by 9, and multiply the numerator and denominator of 5/9 by 13 so both fractions share the common base 117.
Working: 7 × 9/13 × 9 = 63/117 and 5 × 13/9 × 13 = 65/117

Step 3: Add the Numerators
Now add the numerators (63 + 65 = 128) and keep the common denominator 117 unchanged.
Working: 63 + 65/117 = 128/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 128 and 117 is 1, confirming that 128/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 128/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (128) is greater than the denominator (117), divide 128 by 117: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/117.
Working: 128/117 = 1 11/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 128 by denominator 117 produces a repeating decimal (approximately 1.094017, or 109.4017%).
Working: 128 ÷ 117 = 1.094017 (109.4017%)

Key Values:
- Simplified Fraction: 128/117
- Mixed Number Form: 1 11/117
- Decimal Value: 1.094017
- Percentage: 109.4017%

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Solved with FractionsCalc:
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7/13 + 5/9 = 128/117

Simplified Fraction

128/117

Mixed Number

1 11/117

Decimal Value

1.094017

Percentage

109.4017%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 9 = 117.

LCD(13, 9) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 7/13 by 9, and multiply the numerator and denominator of 5/9 by 13 so both fractions share the common base 117.

7 × 9/13 × 9 = 63/117 and 5 × 13/9 × 13 = 65/117

Step 3

Add the Numerators

Now add the numerators (63 + 65 = 128) and keep the common denominator 117 unchanged.

63 + 65/117 = 128/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 128 and 117 is 1, confirming that 128/117 cannot be reduced further—it is already in its simplest irreducible form.

128/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (128) is greater than the denominator (117), divide 128 by 117: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/117.

128/117 = 111/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 128 by denominator 117 produces a repeating decimal (approximately 1.094017, or 109.4017%).

128 ÷ 117 = 1.094017 (109.4017%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`128/117`
Mixed Number Form	`1 11/117`
Decimal Form	`1.094017`
Percentage	`109.4017%`

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Frequently Asked Questions

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

7/13 + 5/9 in simplest fraction form is 128/117 (or 1 11/117 as a mixed number).

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

7/13 + 5/9 converted to a decimal is 1.094017.

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

7/13 + 5/9 expressed as a percentage is 109.4017%.

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

Because the numerator is greater than the denominator, the improper fraction 128/117 can be written as the mixed number 1 11/117.

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

It results in a repeating decimal (approximately 1.094017...) because the denominator contains prime factors other than 2 and 5.