What is 2/28 plus 2/9? (Answer: 37/126)

Exact Answer

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Problem: What is 2/28 plus 2/9?
Formula / Expression: 2/28 + 2/9
Final Answer: 37/126
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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 2/28 by 9, and multiply the numerator and denominator of 2/9 by 28 so both fractions share the common base 252.
Working: 2 × 9/28 × 9 = 18/252 and 2 × 28/9 × 28 = 56/252

Step 3: Add the Numerators
Now add the numerators (18 + 56 = 74) and keep the common denominator 252 unchanged.
Working: 18 + 56/252 = 74/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/252 ÷ 2 = 37/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 126 produces a repeating decimal (approximately 0.293651, or 29.3651%).
Working: 37 ÷ 126 = 0.293651 (29.3651%)

Key Values:
- Simplified Fraction: 37/126
- Mixed Number Form: 37/126
- Decimal Value: 0.293651
- Percentage: 29.3651%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-28-plus-2-9/
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2/28 + 2/9 = 37/126

Simplified Fraction

37/126

Mixed Number

Proper (37/126)

Decimal Value

0.293651

Percentage

29.3651%

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Step-by-Step Solution: 2/28 + 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 2/28 by 9, and multiply the numerator and denominator of 2/9 by 28 so both fractions share the common base 252.

2 × 9/28 × 9 = 18/252 and 2 × 28/9 × 28 = 56/252

Step 3

Add the Numerators

Now add the numerators (18 + 56 = 74) and keep the common denominator 252 unchanged.

18 + 56/252 = 74/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 252, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/252 ÷ 2 = 37/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 126 produces a repeating decimal (approximately 0.293651, or 29.3651%).

37 ÷ 126 = 0.293651 (29.3651%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/126`
Mixed Number Form	`37/126`
Decimal Form	`0.293651`
Percentage	`29.3651%`

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Frequently Asked Questions

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

2/28 + 2/9 in simplest fraction form is 37/126.

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

2/28 + 2/9 converted to a decimal is 0.293651.

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

2/28 + 2/9 expressed as a percentage is 29.3651%.

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

It results in a repeating decimal (approximately 0.293651...) because the denominator contains prime factors other than 2 and 5.