What is 2/9 plus 11/28? (Answer: 155/252)

Exact Answer

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Problem: What is 2/9 plus 11/28?
Formula / Expression: 2/9 + 11/28
Final Answer: 155/252
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 28 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 28 = 252.
Working: LCD(9, 28) = 252

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 2/9 by 28, and multiply the numerator and denominator of 11/28 by 9 so both fractions share the common base 252.
Working: 2 × 28/9 × 28 = 56/252 and 11 × 9/28 × 9 = 99/252

Step 3: Add the Numerators
Now add the numerators (56 + 99 = 155) and keep the common denominator 252 unchanged.
Working: 56 + 99/252 = 155/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 155 and 252 is 1, confirming that 155/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 155/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 155 by denominator 252 produces a repeating decimal (approximately 0.615079, or 61.5079%).
Working: 155 ÷ 252 = 0.615079 (61.5079%)

Key Values:
- Simplified Fraction: 155/252
- Mixed Number Form: 155/252
- Decimal Value: 0.615079
- Percentage: 61.5079%

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Solved with FractionsCalc:
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2/9 + 11/28 = 155/252

Simplified Fraction

155/252

Mixed Number

Proper (155/252)

Decimal Value

0.615079

Percentage

61.5079%

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Step-by-Step Solution: 2/9 + 11/28

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 28 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 28 = 252.

LCD(9, 28) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 2/9 by 28, and multiply the numerator and denominator of 11/28 by 9 so both fractions share the common base 252.

2 × 28/9 × 28 = 56/252 and 11 × 9/28 × 9 = 99/252

Step 3

Add the Numerators

Now add the numerators (56 + 99 = 155) and keep the common denominator 252 unchanged.

56 + 99/252 = 155/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 155 and 252 is 1, confirming that 155/252 cannot be reduced further—it is already in its simplest irreducible form.

155/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 155 by denominator 252 produces a repeating decimal (approximately 0.615079, or 61.5079%).

155 ÷ 252 = 0.615079 (61.5079%)

Visual Representation

The diagram below illustrates 2/9 plus 11/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`155/252`
Mixed Number Form	`155/252`
Decimal Form	`0.615079`
Percentage	`61.5079%`

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Frequently Asked Questions

What is 2/9 plus 11/28 as a fraction?

2/9 + 11/28 in simplest fraction form is 155/252.

What is 2/9 plus 11/28 as a decimal?

2/9 + 11/28 converted to a decimal is 0.615079.

What is 2/9 plus 11/28 as a percentage?

2/9 + 11/28 expressed as a percentage is 61.5079%.

Does 2/9 plus 11/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.615079...) because the denominator contains prime factors other than 2 and 5.