What is 9/13 plus 7/9? (Answer: 172/117)

Exact Answer

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Problem: What is 9/13 plus 7/9?
Formula / Expression: 9/13 + 7/9
Final Answer: 1 55/117 (172/117)
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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 9/13 by 9, and multiply the numerator and denominator of 7/9 by 13 so both fractions share the common base 117.
Working: 9 × 9/13 × 9 = 81/117 and 7 × 13/9 × 13 = 91/117

Step 3: Add the Numerators
Now add the numerators (81 + 91 = 172) and keep the common denominator 117 unchanged.
Working: 81 + 91/117 = 172/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 172 and 117 is 1, confirming that 172/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 172/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (172) is greater than the denominator (117), divide 172 by 117: it goes in 1 whole time(s) with a remainder of 55, giving the mixed number 1 55/117.
Working: 172/117 = 1 55/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 172 by denominator 117 produces a repeating decimal (approximately 1.470085, or 147.0085%).
Working: 172 ÷ 117 = 1.470085 (147.0085%)

Key Values:
- Simplified Fraction: 172/117
- Mixed Number Form: 1 55/117
- Decimal Value: 1.470085
- Percentage: 147.0085%

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Solved with FractionsCalc:
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9/13 + 7/9 = 172/117

Simplified Fraction

172/117

Mixed Number

1 55/117

Decimal Value

1.470085

Percentage

147.0085%

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

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

9 × 9/13 × 9 = 81/117 and 7 × 13/9 × 13 = 91/117

Step 3

Add the Numerators

Now add the numerators (81 + 91 = 172) and keep the common denominator 117 unchanged.

81 + 91/117 = 172/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 172 and 117 is 1, confirming that 172/117 cannot be reduced further—it is already in its simplest irreducible form.

172/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (172) is greater than the denominator (117), divide 172 by 117: it goes in 1 whole time(s) with a remainder of 55, giving the mixed number 1 55/117.

172/117 = 155/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 172 by denominator 117 produces a repeating decimal (approximately 1.470085, or 147.0085%).

172 ÷ 117 = 1.470085 (147.0085%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`172/117`
Mixed Number Form	`1 55/117`
Decimal Form	`1.470085`
Percentage	`147.0085%`

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Frequently Asked Questions

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

9/13 + 7/9 in simplest fraction form is 172/117 (or 1 55/117 as a mixed number).

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

9/13 + 7/9 converted to a decimal is 1.470085.

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

9/13 + 7/9 expressed as a percentage is 147.0085%.

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

Because the numerator is greater than the denominator, the improper fraction 172/117 can be written as the mixed number 1 55/117.

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

It results in a repeating decimal (approximately 1.470085...) because the denominator contains prime factors other than 2 and 5.