What is 9/17 plus 4/5? (Answer: 113/85)

Exact Answer

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Problem: What is 9/17 plus 4/5?
Formula / Expression: 9/17 + 4/5
Final Answer: 1 28/85 (113/85)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 5 = 85.
Working: LCD(17, 5) = 85

Step 2: Convert to Equivalent Fractions with Common Denominator 85
Multiply the numerator and denominator of 9/17 by 5, and multiply the numerator and denominator of 4/5 by 17 so both fractions share the common base 85.
Working: 9 × 5/17 × 5 = 45/85 and 4 × 17/5 × 17 = 68/85

Step 3: Add the Numerators
Now add the numerators (45 + 68 = 113) and keep the common denominator 85 unchanged.
Working: 45 + 68/85 = 113/85

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 85 is 1, confirming that 113/85 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/85

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (113) is greater than the denominator (85), divide 113 by 85: it goes in 1 whole time(s) with a remainder of 28, giving the mixed number 1 28/85.
Working: 113/85 = 1 28/85

Step 6: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 85 produces a repeating decimal (approximately 1.329412, or 132.9412%).
Working: 113 ÷ 85 = 1.329412 (132.9412%)

Key Values:
- Simplified Fraction: 113/85
- Mixed Number Form: 1 28/85
- Decimal Value: 1.329412
- Percentage: 132.9412%

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Solved with FractionsCalc:
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9/17 + 4/5 = 113/85

Simplified Fraction

113/85

Mixed Number

1 28/85

Decimal Value

1.329412

Percentage

132.9412%

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Step-by-Step Solution: 9/17 + 4/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 5 = 85.

LCD(17, 5) = 85

Step 2

Convert to Equivalent Fractions with Common Denominator 85

Multiply the numerator and denominator of 9/17 by 5, and multiply the numerator and denominator of 4/5 by 17 so both fractions share the common base 85.

9 × 5/17 × 5 = 45/85 and 4 × 17/5 × 17 = 68/85

Step 3

Add the Numerators

Now add the numerators (45 + 68 = 113) and keep the common denominator 85 unchanged.

45 + 68/85 = 113/85

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 85 is 1, confirming that 113/85 cannot be reduced further—it is already in its simplest irreducible form.

113/85

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (113) is greater than the denominator (85), divide 113 by 85: it goes in 1 whole time(s) with a remainder of 28, giving the mixed number 1 28/85.

113/85 = 128/85

Step 6

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 85 produces a repeating decimal (approximately 1.329412, or 132.9412%).

113 ÷ 85 = 1.329412 (132.9412%)

Visual Representation

The diagram below illustrates 9/17 plus 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/85`
Mixed Number Form	`1 28/85`
Decimal Form	`1.329412`
Percentage	`132.9412%`

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Frequently Asked Questions

What is 9/17 plus 4/5 as a fraction?

9/17 + 4/5 in simplest fraction form is 113/85 (or 1 28/85 as a mixed number).

What is 9/17 plus 4/5 as a decimal?

9/17 + 4/5 converted to a decimal is 1.329412.

What is 9/17 plus 4/5 as a percentage?

9/17 + 4/5 expressed as a percentage is 132.9412%.

How do you write 9/17 plus 4/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 113/85 can be written as the mixed number 1 28/85.

Does 9/17 plus 4/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.329412...) because the denominator contains prime factors other than 2 and 5.