What is 7/26 plus 2/7? (Answer: 101/182)

Exact Answer

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Problem: What is 7/26 plus 2/7?
Formula / Expression: 7/26 + 2/7
Final Answer: 101/182
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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 7/26 by 7, and multiply the numerator and denominator of 2/7 by 26 so both fractions share the common base 182.
Working: 7 × 7/26 × 7 = 49/182 and 2 × 26/7 × 26 = 52/182

Step 3: Add the Numerators
Now add the numerators (49 + 52 = 101) and keep the common denominator 182 unchanged.
Working: 49 + 52/182 = 101/182

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 182 is 1, confirming that 101/182 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/182

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 182 produces a repeating decimal (approximately 0.554945, or 55.4945%).
Working: 101 ÷ 182 = 0.554945 (55.4945%)

Key Values:
- Simplified Fraction: 101/182
- Mixed Number Form: 101/182
- Decimal Value: 0.554945
- Percentage: 55.4945%

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Solved with FractionsCalc:
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7/26 + 2/7 = 101/182

Simplified Fraction

101/182

Mixed Number

Proper (101/182)

Decimal Value

0.554945

Percentage

55.4945%

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Step-by-Step Solution: 7/26 + 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 7/26 by 7, and multiply the numerator and denominator of 2/7 by 26 so both fractions share the common base 182.

7 × 7/26 × 7 = 49/182 and 2 × 26/7 × 26 = 52/182

Step 3

Add the Numerators

Now add the numerators (49 + 52 = 101) and keep the common denominator 182 unchanged.

49 + 52/182 = 101/182

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 182 is 1, confirming that 101/182 cannot be reduced further—it is already in its simplest irreducible form.

101/182

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 182 produces a repeating decimal (approximately 0.554945, or 55.4945%).

101 ÷ 182 = 0.554945 (55.4945%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/182`
Mixed Number Form	`101/182`
Decimal Form	`0.554945`
Percentage	`55.4945%`

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Frequently Asked Questions

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

7/26 + 2/7 in simplest fraction form is 101/182.

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

7/26 + 2/7 converted to a decimal is 0.554945.

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

7/26 + 2/7 expressed as a percentage is 55.4945%.

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

It results in a repeating decimal (approximately 0.554945...) because the denominator contains prime factors other than 2 and 5.