What is 3/7 plus 9/18? (Answer: 13/14)

Exact Answer

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Problem: What is 3/7 plus 9/18?
Formula / Expression: 3/7 + 9/18
Final Answer: 13/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 18 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 18 = 126.
Working: LCD(7, 18) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 3/7 by 18, and multiply the numerator and denominator of 9/18 by 7 so both fractions share the common base 126.
Working: 3 × 18/7 × 18 = 54/126 and 9 × 7/18 × 7 = 63/126

Step 3: Add the Numerators
Now add the numerators (54 + 63 = 117) and keep the common denominator 126 unchanged.
Working: 54 + 63/126 = 117/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 117 and 126, which is 9. Divide both the numerator and denominator by 9.
Working: 117 ÷ 9/126 ÷ 9 = 13/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 14 produces a repeating decimal (approximately 0.928571, or 92.8571%).
Working: 13 ÷ 14 = 0.928571 (92.8571%)

Key Values:
- Simplified Fraction: 13/14
- Mixed Number Form: 13/14
- Decimal Value: 0.928571
- Percentage: 92.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-9-18/
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3/7 + 9/18 = 13/14

Simplified Fraction

13/14

Mixed Number

Proper (13/14)

Decimal Value

0.928571

Percentage

92.8571%

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Step-by-Step Solution: 3/7 + 9/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 18 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 18 = 126.

LCD(7, 18) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 3/7 by 18, and multiply the numerator and denominator of 9/18 by 7 so both fractions share the common base 126.

3 × 18/7 × 18 = 54/126 and 9 × 7/18 × 7 = 63/126

Step 3

Add the Numerators

Now add the numerators (54 + 63 = 117) and keep the common denominator 126 unchanged.

54 + 63/126 = 117/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 117 and 126, which is 9. Divide both the numerator and denominator by 9.

117 ÷ 9/126 ÷ 9 = 13/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 14 produces a repeating decimal (approximately 0.928571, or 92.8571%).

13 ÷ 14 = 0.928571 (92.8571%)

Visual Representation

The diagram below illustrates 3/7 plus 9/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/14`
Mixed Number Form	`13/14`
Decimal Form	`0.928571`
Percentage	`92.8571%`

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Frequently Asked Questions

What is 3/7 plus 9/18 as a fraction?

3/7 + 9/18 in simplest fraction form is 13/14.

What is 3/7 plus 9/18 as a decimal?

3/7 + 9/18 converted to a decimal is 0.928571.

What is 3/7 plus 9/18 as a percentage?

3/7 + 9/18 expressed as a percentage is 92.8571%.

Does 3/7 plus 9/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.928571...) because the denominator contains prime factors other than 2 and 5.