What is 2/19 plus 5/7? (Answer: 109/133)

Exact Answer

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Problem: What is 2/19 plus 5/7?
Formula / Expression: 2/19 + 5/7
Final Answer: 109/133
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 7 = 133.
Working: LCD(19, 7) = 133

Step 2: Convert to Equivalent Fractions with Common Denominator 133
Multiply the numerator and denominator of 2/19 by 7, and multiply the numerator and denominator of 5/7 by 19 so both fractions share the common base 133.
Working: 2 × 7/19 × 7 = 14/133 and 5 × 19/7 × 19 = 95/133

Step 3: Add the Numerators
Now add the numerators (14 + 95 = 109) and keep the common denominator 133 unchanged.
Working: 14 + 95/133 = 109/133

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 133 is 1, confirming that 109/133 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 133 produces a repeating decimal (approximately 0.819549, or 81.9549%).
Working: 109 ÷ 133 = 0.819549 (81.9549%)

Key Values:
- Simplified Fraction: 109/133
- Mixed Number Form: 109/133
- Decimal Value: 0.819549
- Percentage: 81.9549%

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Solved with FractionsCalc:
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2/19 + 5/7 = 109/133

Simplified Fraction

109/133

Mixed Number

Proper (109/133)

Decimal Value

0.819549

Percentage

81.9549%

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Step-by-Step Solution: 2/19 + 5/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 7 = 133.

LCD(19, 7) = 133

Step 2

Convert to Equivalent Fractions with Common Denominator 133

Multiply the numerator and denominator of 2/19 by 7, and multiply the numerator and denominator of 5/7 by 19 so both fractions share the common base 133.

2 × 7/19 × 7 = 14/133 and 5 × 19/7 × 19 = 95/133

Step 3

Add the Numerators

Now add the numerators (14 + 95 = 109) and keep the common denominator 133 unchanged.

14 + 95/133 = 109/133

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 133 is 1, confirming that 109/133 cannot be reduced further—it is already in its simplest irreducible form.

109/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 133 produces a repeating decimal (approximately 0.819549, or 81.9549%).

109 ÷ 133 = 0.819549 (81.9549%)

Visual Representation

The diagram below illustrates 2/19 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/133`
Mixed Number Form	`109/133`
Decimal Form	`0.819549`
Percentage	`81.9549%`

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Frequently Asked Questions

What is 2/19 plus 5/7 as a fraction?

2/19 + 5/7 in simplest fraction form is 109/133.

What is 2/19 plus 5/7 as a decimal?

2/19 + 5/7 converted to a decimal is 0.819549.

What is 2/19 plus 5/7 as a percentage?

2/19 + 5/7 expressed as a percentage is 81.9549%.

Does 2/19 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.819549...) because the denominator contains prime factors other than 2 and 5.