What is 2/26 plus 4/7? (Answer: 59/91)

Exact Answer

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Problem: What is 2/26 plus 4/7?
Formula / Expression: 2/26 + 4/7
Final Answer: 59/91
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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 2/26 by 7, and multiply the numerator and denominator of 4/7 by 26 so both fractions share the common base 182.
Working: 2 × 7/26 × 7 = 14/182 and 4 × 26/7 × 26 = 104/182

Step 3: Add the Numerators
Now add the numerators (14 + 104 = 118) and keep the common denominator 182 unchanged.
Working: 14 + 104/182 = 118/182

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 118 and 182, which is 2. Divide both the numerator and denominator by 2.
Working: 118 ÷ 2/182 ÷ 2 = 59/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 91 produces a repeating decimal (approximately 0.648352, or 64.8352%).
Working: 59 ÷ 91 = 0.648352 (64.8352%)

Key Values:
- Simplified Fraction: 59/91
- Mixed Number Form: 59/91
- Decimal Value: 0.648352
- Percentage: 64.8352%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-26-plus-4-7/
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2/26 + 4/7 = 59/91

Simplified Fraction

59/91

Mixed Number

Proper (59/91)

Decimal Value

0.648352

Percentage

64.8352%

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Step-by-Step Solution: 2/26 + 4/7

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 2/26 by 7, and multiply the numerator and denominator of 4/7 by 26 so both fractions share the common base 182.

2 × 7/26 × 7 = 14/182 and 4 × 26/7 × 26 = 104/182

Step 3

Add the Numerators

Now add the numerators (14 + 104 = 118) and keep the common denominator 182 unchanged.

14 + 104/182 = 118/182

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 118 and 182, which is 2. Divide both the numerator and denominator by 2.

118 ÷ 2/182 ÷ 2 = 59/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 91 produces a repeating decimal (approximately 0.648352, or 64.8352%).

59 ÷ 91 = 0.648352 (64.8352%)

Visual Representation

The diagram below illustrates 2/26 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/91`
Mixed Number Form	`59/91`
Decimal Form	`0.648352`
Percentage	`64.8352%`

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Frequently Asked Questions

What is 2/26 plus 4/7 as a fraction?

2/26 + 4/7 in simplest fraction form is 59/91.

What is 2/26 plus 4/7 as a decimal?

2/26 + 4/7 converted to a decimal is 0.648352.

What is 2/26 plus 4/7 as a percentage?

2/26 + 4/7 expressed as a percentage is 64.8352%.

Does 2/26 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.648352...) because the denominator contains prime factors other than 2 and 5.