What is 2/28 plus 4/9? (Answer: 65/126)

Exact Answer

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Problem: What is 2/28 plus 4/9?
Formula / Expression: 2/28 + 4/9
Final Answer: 65/126
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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 4/9 by 28 so both fractions share the common base 252.
Working: 2 × 9/28 × 9 = 18/252 and 4 × 28/9 × 28 = 112/252

Step 3: Add the Numerators
Now add the numerators (18 + 112 = 130) and keep the common denominator 252 unchanged.
Working: 18 + 112/252 = 130/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 130 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: 130 ÷ 2/252 ÷ 2 = 65/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 126 produces a repeating decimal (approximately 0.515873, or 51.5873%).
Working: 65 ÷ 126 = 0.515873 (51.5873%)

Key Values:
- Simplified Fraction: 65/126
- Mixed Number Form: 65/126
- Decimal Value: 0.515873
- Percentage: 51.5873%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-28-plus-4-9/
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2/28 + 4/9 = 65/126

Simplified Fraction

65/126

Mixed Number

Proper (65/126)

Decimal Value

0.515873

Percentage

51.5873%

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Step-by-Step Solution: 2/28 + 4/9

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 4/9 by 28 so both fractions share the common base 252.

2 × 9/28 × 9 = 18/252 and 4 × 28/9 × 28 = 112/252

Step 3

Add the Numerators

Now add the numerators (18 + 112 = 130) and keep the common denominator 252 unchanged.

18 + 112/252 = 130/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 130 and 252, which is 2. Divide both the numerator and denominator by 2.

130 ÷ 2/252 ÷ 2 = 65/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 126 produces a repeating decimal (approximately 0.515873, or 51.5873%).

65 ÷ 126 = 0.515873 (51.5873%)

Visual Representation

The diagram below illustrates 2/28 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/126`
Mixed Number Form	`65/126`
Decimal Form	`0.515873`
Percentage	`51.5873%`

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Frequently Asked Questions

What is 2/28 plus 4/9 as a fraction?

2/28 + 4/9 in simplest fraction form is 65/126.

What is 2/28 plus 4/9 as a decimal?

2/28 + 4/9 converted to a decimal is 0.515873.

What is 2/28 plus 4/9 as a percentage?

2/28 + 4/9 expressed as a percentage is 51.5873%.

Does 2/28 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.515873...) because the denominator contains prime factors other than 2 and 5.