What is 3/8 plus 9/17? (Answer: 123/136)

Exact Answer

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Problem: What is 3/8 plus 9/17?
Formula / Expression: 3/8 + 9/17
Final Answer: 123/136
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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 3/8 by 17, and multiply the numerator and denominator of 9/17 by 8 so both fractions share the common base 136.
Working: 3 × 17/8 × 17 = 51/136 and 9 × 8/17 × 8 = 72/136

Step 3: Add the Numerators
Now add the numerators (51 + 72 = 123) and keep the common denominator 136 unchanged.
Working: 51 + 72/136 = 123/136

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 123 and 136 is 1, confirming that 123/136 cannot be reduced further—it is already in its simplest irreducible form.
Working: 123/136

Step 5: Decimal & Percentage Representation
Dividing the numerator 123 by denominator 136 produces a repeating decimal (approximately 0.904412, or 90.4412%).
Working: 123 ÷ 136 = 0.904412 (90.4412%)

Key Values:
- Simplified Fraction: 123/136
- Mixed Number Form: 123/136
- Decimal Value: 0.904412
- Percentage: 90.4412%

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Solved with FractionsCalc:
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3/8 + 9/17 = 123/136

Simplified Fraction

123/136

Mixed Number

Proper (123/136)

Decimal Value

0.904412

Percentage

90.4412%

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Step-by-Step Solution: 3/8 + 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 3/8 by 17, and multiply the numerator and denominator of 9/17 by 8 so both fractions share the common base 136.

3 × 17/8 × 17 = 51/136 and 9 × 8/17 × 8 = 72/136

Step 3

Add the Numerators

Now add the numerators (51 + 72 = 123) and keep the common denominator 136 unchanged.

51 + 72/136 = 123/136

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 123 and 136 is 1, confirming that 123/136 cannot be reduced further—it is already in its simplest irreducible form.

123/136

Step 5

Decimal & Percentage Representation

Dividing the numerator 123 by denominator 136 produces a repeating decimal (approximately 0.904412, or 90.4412%).

123 ÷ 136 = 0.904412 (90.4412%)

Visual Representation

The diagram below illustrates 3/8 plus 9/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`123/136`
Mixed Number Form	`123/136`
Decimal Form	`0.904412`
Percentage	`90.4412%`

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Frequently Asked Questions

What is 3/8 plus 9/17 as a fraction?

3/8 + 9/17 in simplest fraction form is 123/136.

What is 3/8 plus 9/17 as a decimal?

3/8 + 9/17 converted to a decimal is 0.904412.

What is 3/8 plus 9/17 as a percentage?

3/8 + 9/17 expressed as a percentage is 90.4412%.

Does 3/8 plus 9/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.904412...) because the denominator contains prime factors other than 2 and 5.