What is 4/8 plus 9/17? (Answer: 35/34)

Exact Answer

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Problem: What is 4/8 plus 9/17?
Formula / Expression: 4/8 + 9/17
Final Answer: 1 1/34 (35/34)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 17 = 136.
Working: LCD(8, 17) = 136

Step 2: Convert to Equivalent Fractions with Common Denominator 136
Multiply the numerator and denominator of 4/8 by 17, and multiply the numerator and denominator of 9/17 by 8 so both fractions share the common base 136.
Working: 4 × 17/8 × 17 = 68/136 and 9 × 8/17 × 8 = 72/136

Step 3: Add the Numerators
Now add the numerators (68 + 72 = 140) and keep the common denominator 136 unchanged.
Working: 68 + 72/136 = 140/136

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 136, which is 4. Divide both the numerator and denominator by 4.
Working: 140 ÷ 4/136 ÷ 4 = 35/34

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (35) is greater than the denominator (34), divide 35 by 34: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/34.
Working: 35/34 = 1 1/34

Step 6: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 34 produces a repeating decimal (approximately 1.029412, or 102.9412%).
Working: 35 ÷ 34 = 1.029412 (102.9412%)

Key Values:
- Simplified Fraction: 35/34
- Mixed Number Form: 1 1/34
- Decimal Value: 1.029412
- Percentage: 102.9412%

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Solved with FractionsCalc:
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4/8 + 9/17 = 35/34

Simplified Fraction

35/34

Mixed Number

1 1/34

Decimal Value

1.029412

Percentage

102.9412%

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Step-by-Step Solution: 4/8 + 9/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 17 = 136.

LCD(8, 17) = 136

Step 2

Convert to Equivalent Fractions with Common Denominator 136

Multiply the numerator and denominator of 4/8 by 17, and multiply the numerator and denominator of 9/17 by 8 so both fractions share the common base 136.

4 × 17/8 × 17 = 68/136 and 9 × 8/17 × 8 = 72/136

Step 3

Add the Numerators

Now add the numerators (68 + 72 = 140) and keep the common denominator 136 unchanged.

68 + 72/136 = 140/136

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 136, which is 4. Divide both the numerator and denominator by 4.

140 ÷ 4/136 ÷ 4 = 35/34

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (35) is greater than the denominator (34), divide 35 by 34: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/34.

35/34 = 11/34

Step 6

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 34 produces a repeating decimal (approximately 1.029412, or 102.9412%).

35 ÷ 34 = 1.029412 (102.9412%)

Visual Representation

The diagram below illustrates 4/8 plus 9/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/34`
Mixed Number Form	`1 1/34`
Decimal Form	`1.029412`
Percentage	`102.9412%`

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Frequently Asked Questions

What is 4/8 plus 9/17 as a fraction?

4/8 + 9/17 in simplest fraction form is 35/34 (or 1 1/34 as a mixed number).

What is 4/8 plus 9/17 as a decimal?

4/8 + 9/17 converted to a decimal is 1.029412.

What is 4/8 plus 9/17 as a percentage?

4/8 + 9/17 expressed as a percentage is 102.9412%.

How do you write 4/8 plus 9/17 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 35/34 can be written as the mixed number 1 1/34.

Does 4/8 plus 9/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.029412...) because the denominator contains prime factors other than 2 and 5.