What is 2/18 plus 9/49? (Answer: 130/441)

Exact Answer

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Problem: What is 2/18 plus 9/49?
Formula / Expression: 2/18 + 9/49
Final Answer: 130/441
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 49 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 49 = 882.
Working: LCD(18, 49) = 882

Step 2: Convert to Equivalent Fractions with Common Denominator 882
Multiply the numerator and denominator of 2/18 by 49, and multiply the numerator and denominator of 9/49 by 18 so both fractions share the common base 882.
Working: 2 × 49/18 × 49 = 98/882 and 9 × 18/49 × 18 = 162/882

Step 3: Add the Numerators
Now add the numerators (98 + 162 = 260) and keep the common denominator 882 unchanged.
Working: 98 + 162/882 = 260/882

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 260 and 882, which is 2. Divide both the numerator and denominator by 2.
Working: 260 ÷ 2/882 ÷ 2 = 130/441

Step 5: Decimal & Percentage Representation
Dividing the numerator 130 by denominator 441 produces a repeating decimal (approximately 0.294785, or 29.4785%).
Working: 130 ÷ 441 = 0.294785 (29.4785%)

Key Values:
- Simplified Fraction: 130/441
- Mixed Number Form: 130/441
- Decimal Value: 0.294785
- Percentage: 29.4785%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-18-plus-9-49/
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2/18 + 9/49 = 130/441

Simplified Fraction

130/441

Mixed Number

Proper (130/441)

Decimal Value

0.294785

Percentage

29.4785%

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Step-by-Step Solution: 2/18 + 9/49

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 49 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 49 = 882.

LCD(18, 49) = 882

Step 2

Convert to Equivalent Fractions with Common Denominator 882

Multiply the numerator and denominator of 2/18 by 49, and multiply the numerator and denominator of 9/49 by 18 so both fractions share the common base 882.

2 × 49/18 × 49 = 98/882 and 9 × 18/49 × 18 = 162/882

Step 3

Add the Numerators

Now add the numerators (98 + 162 = 260) and keep the common denominator 882 unchanged.

98 + 162/882 = 260/882

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 260 and 882, which is 2. Divide both the numerator and denominator by 2.

260 ÷ 2/882 ÷ 2 = 130/441

Step 5

Decimal & Percentage Representation

Dividing the numerator 130 by denominator 441 produces a repeating decimal (approximately 0.294785, or 29.4785%).

130 ÷ 441 = 0.294785 (29.4785%)

Visual Representation

The diagram below illustrates 2/18 plus 9/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`130/441`
Mixed Number Form	`130/441`
Decimal Form	`0.294785`
Percentage	`29.4785%`

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Frequently Asked Questions

What is 2/18 plus 9/49 as a fraction?

2/18 + 9/49 in simplest fraction form is 130/441.

What is 2/18 plus 9/49 as a decimal?

2/18 + 9/49 converted to a decimal is 0.294785.

What is 2/18 plus 9/49 as a percentage?

2/18 + 9/49 expressed as a percentage is 29.4785%.

Does 2/18 plus 9/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.294785...) because the denominator contains prime factors other than 2 and 5.