What is 5/28 plus 2/9? (Answer: 101/252)

Exact Answer

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Problem: What is 5/28 plus 2/9?
Formula / Expression: 5/28 + 2/9
Final Answer: 101/252
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 5/28 by 9, and multiply the numerator and denominator of 2/9 by 28 so both fractions share the common base 252.
Working: 5 × 9/28 × 9 = 45/252 and 2 × 28/9 × 28 = 56/252

Step 3: Add the Numerators
Now add the numerators (45 + 56 = 101) and keep the common denominator 252 unchanged.
Working: 45 + 56/252 = 101/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 252 is 1, confirming that 101/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 252 produces a repeating decimal (approximately 0.400794, or 40.0794%).
Working: 101 ÷ 252 = 0.400794 (40.0794%)

Key Values:
- Simplified Fraction: 101/252
- Mixed Number Form: 101/252
- Decimal Value: 0.400794
- Percentage: 40.0794%

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5/28 + 2/9 = 101/252

Simplified Fraction

101/252

Mixed Number

Proper (101/252)

Decimal Value

0.400794

Percentage

40.0794%

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Step-by-Step Solution: 5/28 + 2/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(28, 9) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 5/28 by 9, and multiply the numerator and denominator of 2/9 by 28 so both fractions share the common base 252.

5 × 9/28 × 9 = 45/252 and 2 × 28/9 × 28 = 56/252

Step 3

Add the Numerators

Now add the numerators (45 + 56 = 101) and keep the common denominator 252 unchanged.

45 + 56/252 = 101/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 252 is 1, confirming that 101/252 cannot be reduced further—it is already in its simplest irreducible form.

101/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 252 produces a repeating decimal (approximately 0.400794, or 40.0794%).

101 ÷ 252 = 0.400794 (40.0794%)

Visual Representation

The diagram below illustrates 5/28 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/252`
Mixed Number Form	`101/252`
Decimal Form	`0.400794`
Percentage	`40.0794%`

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Frequently Asked Questions

What is 5/28 plus 2/9 as a fraction?

5/28 + 2/9 in simplest fraction form is 101/252.

What is 5/28 plus 2/9 as a decimal?

5/28 + 2/9 converted to a decimal is 0.400794.

What is 5/28 plus 2/9 as a percentage?

5/28 + 2/9 expressed as a percentage is 40.0794%.

Does 5/28 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.400794...) because the denominator contains prime factors other than 2 and 5.