What is 1/9 plus 9/28? (Answer: 109/252)

Exact Answer

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Problem: What is 1/9 plus 9/28?
Formula / Expression: 1/9 + 9/28
Final Answer: 109/252
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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 1/9 by 28, and multiply the numerator and denominator of 9/28 by 9 so both fractions share the common base 252.
Working: 1 × 28/9 × 28 = 28/252 and 9 × 9/28 × 9 = 81/252

Step 3: Add the Numerators
Now add the numerators (28 + 81 = 109) and keep the common denominator 252 unchanged.
Working: 28 + 81/252 = 109/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 252 is 1, confirming that 109/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 252 produces a repeating decimal (approximately 0.43254, or 43.254%).
Working: 109 ÷ 252 = 0.43254 (43.254%)

Key Values:
- Simplified Fraction: 109/252
- Mixed Number Form: 109/252
- Decimal Value: 0.43254
- Percentage: 43.254%

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Solved with FractionsCalc:
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1/9 + 9/28 = 109/252

Simplified Fraction

109/252

Mixed Number

Proper (109/252)

Decimal Value

0.43254

Percentage

43.254%

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Step-by-Step Solution: 1/9 + 9/28

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 1/9 by 28, and multiply the numerator and denominator of 9/28 by 9 so both fractions share the common base 252.

1 × 28/9 × 28 = 28/252 and 9 × 9/28 × 9 = 81/252

Step 3

Add the Numerators

Now add the numerators (28 + 81 = 109) and keep the common denominator 252 unchanged.

28 + 81/252 = 109/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 252 is 1, confirming that 109/252 cannot be reduced further—it is already in its simplest irreducible form.

109/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 252 produces a repeating decimal (approximately 0.43254, or 43.254%).

109 ÷ 252 = 0.43254 (43.254%)

Visual Representation

The diagram below illustrates 1/9 plus 9/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/252`
Mixed Number Form	`109/252`
Decimal Form	`0.43254`
Percentage	`43.254%`

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Frequently Asked Questions

What is 1/9 plus 9/28 as a fraction?

1/9 + 9/28 in simplest fraction form is 109/252.

What is 1/9 plus 9/28 as a decimal?

1/9 + 9/28 converted to a decimal is 0.43254.

What is 1/9 plus 9/28 as a percentage?

1/9 + 9/28 expressed as a percentage is 43.254%.

Does 1/9 plus 9/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.43254...) because the denominator contains prime factors other than 2 and 5.