What is 2/9 plus 10/28? (Answer: 73/126)

Exact Answer

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Problem: What is 2/9 plus 10/28?
Formula / Expression: 2/9 + 10/28
Final Answer: 73/126
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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 10/28 by 9 so both fractions share the common base 252.
Working: 2 × 28/9 × 28 = 56/252 and 10 × 9/28 × 9 = 90/252

Step 3: Add the Numerators
Now add the numerators (56 + 90 = 146) and keep the common denominator 252 unchanged.
Working: 56 + 90/252 = 146/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 146 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: 146 ÷ 2/252 ÷ 2 = 73/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 126 produces a repeating decimal (approximately 0.579365, or 57.9365%).
Working: 73 ÷ 126 = 0.579365 (57.9365%)

Key Values:
- Simplified Fraction: 73/126
- Mixed Number Form: 73/126
- Decimal Value: 0.579365
- Percentage: 57.9365%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-10-28/
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2/9 + 10/28 = 73/126

Simplified Fraction

73/126

Mixed Number

Proper (73/126)

Decimal Value

0.579365

Percentage

57.9365%

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Step-by-Step Solution: 2/9 + 10/28

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 10/28 by 9 so both fractions share the common base 252.

2 × 28/9 × 28 = 56/252 and 10 × 9/28 × 9 = 90/252

Step 3

Add the Numerators

Now add the numerators (56 + 90 = 146) and keep the common denominator 252 unchanged.

56 + 90/252 = 146/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 146 and 252, which is 2. Divide both the numerator and denominator by 2.

146 ÷ 2/252 ÷ 2 = 73/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 126 produces a repeating decimal (approximately 0.579365, or 57.9365%).

73 ÷ 126 = 0.579365 (57.9365%)

Visual Representation

The diagram below illustrates 2/9 plus 10/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/126`
Mixed Number Form	`73/126`
Decimal Form	`0.579365`
Percentage	`57.9365%`

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Frequently Asked Questions

What is 2/9 plus 10/28 as a fraction?

2/9 + 10/28 in simplest fraction form is 73/126.

What is 2/9 plus 10/28 as a decimal?

2/9 + 10/28 converted to a decimal is 0.579365.

What is 2/9 plus 10/28 as a percentage?

2/9 + 10/28 expressed as a percentage is 57.9365%.

Does 2/9 plus 10/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.579365...) because the denominator contains prime factors other than 2 and 5.