What is 3/9 plus 7/17? (Answer: 38/51)

Exact Answer

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Problem: What is 3/9 plus 7/17?
Formula / Expression: 3/9 + 7/17
Final Answer: 38/51
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 17 = 153.
Working: LCD(9, 17) = 153

Step 2: Convert to Equivalent Fractions with Common Denominator 153
Multiply the numerator and denominator of 3/9 by 17, and multiply the numerator and denominator of 7/17 by 9 so both fractions share the common base 153.
Working: 3 × 17/9 × 17 = 51/153 and 7 × 9/17 × 9 = 63/153

Step 3: Add the Numerators
Now add the numerators (51 + 63 = 114) and keep the common denominator 153 unchanged.
Working: 51 + 63/153 = 114/153

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 153, which is 3. Divide both the numerator and denominator by 3.
Working: 114 ÷ 3/153 ÷ 3 = 38/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 51 produces a repeating decimal (approximately 0.745098, or 74.5098%).
Working: 38 ÷ 51 = 0.745098 (74.5098%)

Key Values:
- Simplified Fraction: 38/51
- Mixed Number Form: 38/51
- Decimal Value: 0.745098
- Percentage: 74.5098%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-7-17/
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3/9 + 7/17 = 38/51

Simplified Fraction

38/51

Mixed Number

Proper (38/51)

Decimal Value

0.745098

Percentage

74.5098%

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Step-by-Step Solution: 3/9 + 7/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 17 = 153.

LCD(9, 17) = 153

Step 2

Convert to Equivalent Fractions with Common Denominator 153

Multiply the numerator and denominator of 3/9 by 17, and multiply the numerator and denominator of 7/17 by 9 so both fractions share the common base 153.

3 × 17/9 × 17 = 51/153 and 7 × 9/17 × 9 = 63/153

Step 3

Add the Numerators

Now add the numerators (51 + 63 = 114) and keep the common denominator 153 unchanged.

51 + 63/153 = 114/153

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 153, which is 3. Divide both the numerator and denominator by 3.

114 ÷ 3/153 ÷ 3 = 38/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 51 produces a repeating decimal (approximately 0.745098, or 74.5098%).

38 ÷ 51 = 0.745098 (74.5098%)

Visual Representation

The diagram below illustrates 3/9 plus 7/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/51`
Mixed Number Form	`38/51`
Decimal Form	`0.745098`
Percentage	`74.5098%`

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Frequently Asked Questions

What is 3/9 plus 7/17 as a fraction?

3/9 + 7/17 in simplest fraction form is 38/51.

What is 3/9 plus 7/17 as a decimal?

3/9 + 7/17 converted to a decimal is 0.745098.

What is 3/9 plus 7/17 as a percentage?

3/9 + 7/17 expressed as a percentage is 74.5098%.

Does 3/9 plus 7/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.745098...) because the denominator contains prime factors other than 2 and 5.