What is 5/26 plus 2/7? (Answer: 87/182)

Exact Answer

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Problem: What is 5/26 plus 2/7?
Formula / Expression: 5/26 + 2/7
Final Answer: 87/182
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 7 = 182.
Working: LCD(26, 7) = 182

Step 2: Convert to Equivalent Fractions with Common Denominator 182
Multiply the numerator and denominator of 5/26 by 7, and multiply the numerator and denominator of 2/7 by 26 so both fractions share the common base 182.
Working: 5 × 7/26 × 7 = 35/182 and 2 × 26/7 × 26 = 52/182

Step 3: Add the Numerators
Now add the numerators (35 + 52 = 87) and keep the common denominator 182 unchanged.
Working: 35 + 52/182 = 87/182

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 87 and 182 is 1, confirming that 87/182 cannot be reduced further—it is already in its simplest irreducible form.
Working: 87/182

Step 5: Decimal & Percentage Representation
Dividing the numerator 87 by denominator 182 produces a repeating decimal (approximately 0.478022, or 47.8022%).
Working: 87 ÷ 182 = 0.478022 (47.8022%)

Key Values:
- Simplified Fraction: 87/182
- Mixed Number Form: 87/182
- Decimal Value: 0.478022
- Percentage: 47.8022%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-26-plus-2-7/
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5/26 + 2/7 = 87/182

Simplified Fraction

87/182

Mixed Number

Proper (87/182)

Decimal Value

0.478022

Percentage

47.8022%

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Step-by-Step Solution: 5/26 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 7 = 182.

LCD(26, 7) = 182

Step 2

Convert to Equivalent Fractions with Common Denominator 182

Multiply the numerator and denominator of 5/26 by 7, and multiply the numerator and denominator of 2/7 by 26 so both fractions share the common base 182.

5 × 7/26 × 7 = 35/182 and 2 × 26/7 × 26 = 52/182

Step 3

Add the Numerators

Now add the numerators (35 + 52 = 87) and keep the common denominator 182 unchanged.

35 + 52/182 = 87/182

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 87 and 182 is 1, confirming that 87/182 cannot be reduced further—it is already in its simplest irreducible form.

87/182

Step 5

Decimal & Percentage Representation

Dividing the numerator 87 by denominator 182 produces a repeating decimal (approximately 0.478022, or 47.8022%).

87 ÷ 182 = 0.478022 (47.8022%)

Visual Representation

The diagram below illustrates 5/26 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`87/182`
Mixed Number Form	`87/182`
Decimal Form	`0.478022`
Percentage	`47.8022%`

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Frequently Asked Questions

What is 5/26 plus 2/7 as a fraction?

5/26 + 2/7 in simplest fraction form is 87/182.

What is 5/26 plus 2/7 as a decimal?

5/26 + 2/7 converted to a decimal is 0.478022.

What is 5/26 plus 2/7 as a percentage?

5/26 + 2/7 expressed as a percentage is 47.8022%.

Does 5/26 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.478022...) because the denominator contains prime factors other than 2 and 5.