What is 2/56 plus 2/9? (Answer: 65/252)

Exact Answer

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Problem: What is 2/56 plus 2/9?
Formula / Expression: 2/56 + 2/9
Final Answer: 65/252
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 56 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 56 × 9 = 504.
Working: LCD(56, 9) = 504

Step 2: Convert to Equivalent Fractions with Common Denominator 504
Multiply the numerator and denominator of 2/56 by 9, and multiply the numerator and denominator of 2/9 by 56 so both fractions share the common base 504.
Working: 2 × 9/56 × 9 = 18/504 and 2 × 56/9 × 56 = 112/504

Step 3: Add the Numerators
Now add the numerators (18 + 112 = 130) and keep the common denominator 504 unchanged.
Working: 18 + 112/504 = 130/504

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 130 and 504, which is 2. Divide both the numerator and denominator by 2.
Working: 130 ÷ 2/504 ÷ 2 = 65/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 252 produces a repeating decimal (approximately 0.257937, or 25.7937%).
Working: 65 ÷ 252 = 0.257937 (25.7937%)

Key Values:
- Simplified Fraction: 65/252
- Mixed Number Form: 65/252
- Decimal Value: 0.257937
- Percentage: 25.7937%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-56-plus-2-9/
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2/56 + 2/9 = 65/252

Simplified Fraction

65/252

Mixed Number

Proper (65/252)

Decimal Value

0.257937

Percentage

25.7937%

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Step-by-Step Solution: 2/56 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 56 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 56 × 9 = 504.

LCD(56, 9) = 504

Step 2

Convert to Equivalent Fractions with Common Denominator 504

Multiply the numerator and denominator of 2/56 by 9, and multiply the numerator and denominator of 2/9 by 56 so both fractions share the common base 504.

2 × 9/56 × 9 = 18/504 and 2 × 56/9 × 56 = 112/504

Step 3

Add the Numerators

Now add the numerators (18 + 112 = 130) and keep the common denominator 504 unchanged.

18 + 112/504 = 130/504

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 130 and 504, which is 2. Divide both the numerator and denominator by 2.

130 ÷ 2/504 ÷ 2 = 65/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 252 produces a repeating decimal (approximately 0.257937, or 25.7937%).

65 ÷ 252 = 0.257937 (25.7937%)

Visual Representation

The diagram below illustrates 2/56 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/252`
Mixed Number Form	`65/252`
Decimal Form	`0.257937`
Percentage	`25.7937%`

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Frequently Asked Questions

What is 2/56 plus 2/9 as a fraction?

2/56 + 2/9 in simplest fraction form is 65/252.

What is 2/56 plus 2/9 as a decimal?

2/56 + 2/9 converted to a decimal is 0.257937.

What is 2/56 plus 2/9 as a percentage?

2/56 + 2/9 expressed as a percentage is 25.7937%.

Does 2/56 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.257937...) because the denominator contains prime factors other than 2 and 5.