What is 2/6 plus 7/19? (Answer: 40/57)

Exact Answer

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Problem: What is 2/6 plus 7/19?
Formula / Expression: 2/6 + 7/19
Final Answer: 40/57
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 19 = 114.
Working: LCD(6, 19) = 114

Step 2: Convert to Equivalent Fractions with Common Denominator 114
Multiply the numerator and denominator of 2/6 by 19, and multiply the numerator and denominator of 7/19 by 6 so both fractions share the common base 114.
Working: 2 × 19/6 × 19 = 38/114 and 7 × 6/19 × 6 = 42/114

Step 3: Add the Numerators
Now add the numerators (38 + 42 = 80) and keep the common denominator 114 unchanged.
Working: 38 + 42/114 = 80/114

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 80 and 114, which is 2. Divide both the numerator and denominator by 2.
Working: 80 ÷ 2/114 ÷ 2 = 40/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 57 produces a repeating decimal (approximately 0.701754, or 70.1754%).
Working: 40 ÷ 57 = 0.701754 (70.1754%)

Key Values:
- Simplified Fraction: 40/57
- Mixed Number Form: 40/57
- Decimal Value: 0.701754
- Percentage: 70.1754%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-6-plus-7-19/
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2/6 + 7/19 = 40/57

Simplified Fraction

40/57

Mixed Number

Proper (40/57)

Decimal Value

0.701754

Percentage

70.1754%

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Step-by-Step Solution: 2/6 + 7/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 19 = 114.

LCD(6, 19) = 114

Step 2

Convert to Equivalent Fractions with Common Denominator 114

Multiply the numerator and denominator of 2/6 by 19, and multiply the numerator and denominator of 7/19 by 6 so both fractions share the common base 114.

2 × 19/6 × 19 = 38/114 and 7 × 6/19 × 6 = 42/114

Step 3

Add the Numerators

Now add the numerators (38 + 42 = 80) and keep the common denominator 114 unchanged.

38 + 42/114 = 80/114

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 80 and 114, which is 2. Divide both the numerator and denominator by 2.

80 ÷ 2/114 ÷ 2 = 40/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 57 produces a repeating decimal (approximately 0.701754, or 70.1754%).

40 ÷ 57 = 0.701754 (70.1754%)

Visual Representation

The diagram below illustrates 2/6 plus 7/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/57`
Mixed Number Form	`40/57`
Decimal Form	`0.701754`
Percentage	`70.1754%`

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Frequently Asked Questions

What is 2/6 plus 7/19 as a fraction?

2/6 + 7/19 in simplest fraction form is 40/57.

What is 2/6 plus 7/19 as a decimal?

2/6 + 7/19 converted to a decimal is 0.701754.

What is 2/6 plus 7/19 as a percentage?

2/6 + 7/19 expressed as a percentage is 70.1754%.

Does 2/6 plus 7/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.701754...) because the denominator contains prime factors other than 2 and 5.