What is 5/49 plus 2/9? (Answer: 143/441)

Exact Answer

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Problem: What is 5/49 plus 2/9?
Formula / Expression: 5/49 + 2/9
Final Answer: 143/441
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 9 = 441.
Working: LCD(49, 9) = 441

Step 2: Convert to Equivalent Fractions with Common Denominator 441
Multiply the numerator and denominator of 5/49 by 9, and multiply the numerator and denominator of 2/9 by 49 so both fractions share the common base 441.
Working: 5 × 9/49 × 9 = 45/441 and 2 × 49/9 × 49 = 98/441

Step 3: Add the Numerators
Now add the numerators (45 + 98 = 143) and keep the common denominator 441 unchanged.
Working: 45 + 98/441 = 143/441

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 441 is 1, confirming that 143/441 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/441

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 441 produces a repeating decimal (approximately 0.324263, or 32.4263%).
Working: 143 ÷ 441 = 0.324263 (32.4263%)

Key Values:
- Simplified Fraction: 143/441
- Mixed Number Form: 143/441
- Decimal Value: 0.324263
- Percentage: 32.4263%

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Solved with FractionsCalc:
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5/49 + 2/9 = 143/441

Simplified Fraction

143/441

Mixed Number

Proper (143/441)

Decimal Value

0.324263

Percentage

32.4263%

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Step-by-Step Solution: 5/49 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 9 = 441.

LCD(49, 9) = 441

Step 2

Convert to Equivalent Fractions with Common Denominator 441

Multiply the numerator and denominator of 5/49 by 9, and multiply the numerator and denominator of 2/9 by 49 so both fractions share the common base 441.

5 × 9/49 × 9 = 45/441 and 2 × 49/9 × 49 = 98/441

Step 3

Add the Numerators

Now add the numerators (45 + 98 = 143) and keep the common denominator 441 unchanged.

45 + 98/441 = 143/441

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 441 is 1, confirming that 143/441 cannot be reduced further—it is already in its simplest irreducible form.

143/441

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 441 produces a repeating decimal (approximately 0.324263, or 32.4263%).

143 ÷ 441 = 0.324263 (32.4263%)

Visual Representation

The diagram below illustrates 5/49 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/441`
Mixed Number Form	`143/441`
Decimal Form	`0.324263`
Percentage	`32.4263%`

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Frequently Asked Questions

What is 5/49 plus 2/9 as a fraction?

5/49 + 2/9 in simplest fraction form is 143/441.

What is 5/49 plus 2/9 as a decimal?

5/49 + 2/9 converted to a decimal is 0.324263.

What is 5/49 plus 2/9 as a percentage?

5/49 + 2/9 expressed as a percentage is 32.4263%.

Does 5/49 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.324263...) because the denominator contains prime factors other than 2 and 5.