What is 7/9 plus 11/13? (Answer: 190/117)

Exact Answer

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Problem: What is 7/9 plus 11/13?
Formula / Expression: 7/9 + 11/13
Final Answer: 1 73/117 (190/117)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 7/9 by 13, and multiply the numerator and denominator of 11/13 by 9 so both fractions share the common base 117.
Working: 7 × 13/9 × 13 = 91/117 and 11 × 9/13 × 9 = 99/117

Step 3: Add the Numerators
Now add the numerators (91 + 99 = 190) and keep the common denominator 117 unchanged.
Working: 91 + 99/117 = 190/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 190 and 117 is 1, confirming that 190/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 190/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (190) is greater than the denominator (117), divide 190 by 117: it goes in 1 whole time(s) with a remainder of 73, giving the mixed number 1 73/117.
Working: 190/117 = 1 73/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 190 by denominator 117 produces a repeating decimal (approximately 1.623932, or 162.3932%).
Working: 190 ÷ 117 = 1.623932 (162.3932%)

Key Values:
- Simplified Fraction: 190/117
- Mixed Number Form: 1 73/117
- Decimal Value: 1.623932
- Percentage: 162.3932%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-9-plus-11-13/
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7/9 + 11/13 = 190/117

Simplified Fraction

190/117

Mixed Number

1 73/117

Decimal Value

1.623932

Percentage

162.3932%

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Step-by-Step Solution: 7/9 + 11/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 13) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 7/9 by 13, and multiply the numerator and denominator of 11/13 by 9 so both fractions share the common base 117.

7 × 13/9 × 13 = 91/117 and 11 × 9/13 × 9 = 99/117

Step 3

Add the Numerators

Now add the numerators (91 + 99 = 190) and keep the common denominator 117 unchanged.

91 + 99/117 = 190/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 190 and 117 is 1, confirming that 190/117 cannot be reduced further—it is already in its simplest irreducible form.

190/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (190) is greater than the denominator (117), divide 190 by 117: it goes in 1 whole time(s) with a remainder of 73, giving the mixed number 1 73/117.

190/117 = 173/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 190 by denominator 117 produces a repeating decimal (approximately 1.623932, or 162.3932%).

190 ÷ 117 = 1.623932 (162.3932%)

Visual Representation

The diagram below illustrates 7/9 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`190/117`
Mixed Number Form	`1 73/117`
Decimal Form	`1.623932`
Percentage	`162.3932%`

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Frequently Asked Questions

What is 7/9 plus 11/13 as a fraction?

7/9 + 11/13 in simplest fraction form is 190/117 (or 1 73/117 as a mixed number).

What is 7/9 plus 11/13 as a decimal?

7/9 + 11/13 converted to a decimal is 1.623932.

What is 7/9 plus 11/13 as a percentage?

7/9 + 11/13 expressed as a percentage is 162.3932%.

How do you write 7/9 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 190/117 can be written as the mixed number 1 73/117.

Does 7/9 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.623932...) because the denominator contains prime factors other than 2 and 5.